2024-03-28T09:37:13Z
https://eprints.maths.manchester.ac.uk/cgi/oai2
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:99
2017-10-20T14:12:02Z
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Longitudinal and Cross-Sectional Analysis of Cytotoxic T Lymphocyte (CTL) Responses and their Relationship to Vertical HIV Transmission
Jin, Xia
Roberts, Caroline G. P.
Nixon, Douglas F.
Cao, Yunzhen
Ho, David D.
Walker, Bruce D.
Muldoon, Mark
Korber, Bette T. M.
Koup, Richard A.
ARIEL Project Investigators, the
62 Statistics
92 Biology and other natural sciences
The ARIEL Project for the Prevention of HIV Transmission from Mother to Infant was established to evaluate virologic and immunologic parameters during vertical transmission. To determine the strength and breadth of the cytotoxic T lymphocyte (CTL) response and its correlation with human immunodeficiency virus (HIV) transmission, a cross-sectional study was done of 31 HIV-infected pregnant women, of whom 15 transmitted and 16 did not transmit HIV to their infants. The precursor frequencies of CTL specific for HIV-1 gag, pol, nef, and env from 5 different isolates of the clade B of HIV-1 were determined by limiting dilution analysis. Results showed that variable levels of HIV-specific CTL response were present in HIV-infected pregnant women during and after pregnancy. In addition, CTL precursor frequencies specific for pol and nef were higher during pregnancy in nontransmitters than in transmitters. Thus, CTL responding to different HIV antigens may not be contributing equally to the prevention of vertical transmission.
1998-11
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/99/1/journal/issues/v178n5/980240/980240.web.pdf
Jin, Xia and Roberts, Caroline G. P. and Nixon, Douglas F. and Cao, Yunzhen and Ho, David D. and Walker, Bruce D. and Muldoon, Mark and Korber, Bette T. M. and Koup, Richard A. and ARIEL Project Investigators, the (1998) Longitudinal and Cross-Sectional Analysis of Cytotoxic T Lymphocyte (CTL) Responses and their Relationship to Vertical HIV Transmission. Journal of Infectious Diseases, 178 (5). pp. 1317-1326. ISSN 0022-1899
http://www.journals.uchicago.edu/JID/journal/issues/v178n5/980240/980240.html
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:120
2017-11-08T23:18:16Z
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https://eprints.maths.manchester.ac.uk/120/
Universal connection and curvature for statistical manifold geometry
Arwini, Khadiga
Del Riego, L
Dodson, CTJ
53 Differential geometry
62 Statistics
Statistical manifolds are representations of smooth families of
probability density functions
that allow differential geometric methods to be applied to
problems in stochastic processes, mathematical statistics and
information theory. It is common to have to consider a number of
linear connections on a given statistical manifold and so it is
important to know the corresponding universal connection and
curvature; then all linear connections and their curvatures are
pullbacks. An important class of statistical manifolds is that
arising from the exponential families and one particular family is
that of gamma distributions, which we showed recently to have
important uniqueness properties in stochastic processes. Here we
provide formulae for universal connections and curvatures on
exponential families and give an explicit example for the manifold
of gamma distributions.
2005
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/120/1/univconexpf.pdf
Arwini, Khadiga and Del Riego, L and Dodson, CTJ (2005) Universal connection and curvature for statistical manifold geometry. Houston Journal of Mathematics, In pre. ISSN 0362-1588 (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:181
2017-10-20T14:12:04Z
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https://eprints.maths.manchester.ac.uk/181/
The Trap of Complacency in Predicting the Maximum
du Toit, Jacques
Peskir, Goran
35 Partial differential equations
45 Integral equations
60 Probability theory and stochastic processes
62 Statistics
2007
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/181/1/2006.30.pdf
du Toit, Jacques and Peskir, Goran (2007) The Trap of Complacency in Predicting the Maximum. Ann. Probability, 35. pp. 340-365.
10.1214/009117906000000638
10.1214/009117906000000638
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:186
2017-11-08T18:18:29Z
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https://eprints.maths.manchester.ac.uk/186/
Recursive estimation and order determination of
space-time autoregressive processes
Antunes, Ana Monica C.
Quinn, Barry, G
Subba Rao, T
62 Statistics
Space-time autoregressive moving average models may be used for time series measured at
the same times in a number of locations. In this paper we propose a recursive algorithm
for estimating space-time autoregressive (AR) models. We also propose an information
criterion for estimating the model order, and prove its strong consistency. The methods are
illustrated using both simulated and real data. The real data corresponds to hourly carbon
monoxide (CO) concentrations recorded in September 1995 at four different locations in
Venice.
2006-03-21
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/186/1/psrr04-2005.pdf
Antunes, Ana Monica C. and Quinn, Barry, G and Subba Rao, T (2006) Recursive estimation and order determination of space-time autoregressive processes. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:187
2017-11-08T18:18:29Z
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https://eprints.maths.manchester.ac.uk/187/
Statistical Analysis and Time Series Models for
Minimum/Maximum Temperatures
in the Antarctic Peninsula
Hughes, Gillian
Subba Rao, T
62 Statistics
Our object in this paper is to study the temperature variations in the Antarctic
Peninsula using multiple regression models with correlated errors admitting ARMA
models with nonGaussian innovations. We found that the Øtted models adequately
describe the variations. The data we consider are minimum/maximum monthly
temperatures recorded at the Faraday station by the British Antarctic Survey for
the period from January 1951 to December 1995. The time series models considered
here are novel in the sense that the linear ARMA models have innovations which
have extreme value distributions, and the maximum likelihood estimation described
here can be widely used in many disciplines.
The time series models we Øtted indicate that the mean of the minimum temperatures
is likely to increase over the next 50 years and the temperatures will
be above 0oC during the summer months which means that the melting season
will increase, creating more climatic and ecological problems. Although the mean
temperature is reported to have increased by 2.5oC we believe that the maximum
temperatures have remained unchanged over the past 45 years. This has led to a
decrease in the diurnal temperature range which has also been observed in many
other parts of the globe.
The in°uence of human activity on climate is still unknown but our ability
to perturb the ozone layer is an established fact. We established a relationship
between minimum monthly temperatures and ozone levels and found they are highly
negatively correlated (at a lag of one month) implying that the higher levels of
ozone in the air keep temperatures low. This resulted in a new time series model
relating the minimum temperatures to ozone levels. After appropriate statistical
tests, we have come to the conclusion that the observed increase in the minimum
temperatures is a consequence of human activity rather than natural causes and
so a reduction in the production of \greenhouse gases" could lead to a decrease in
minimum temperatures, thereby reducing the adverse eÆect of global warming in
the Antarctic Peninsula.
2006-03-21
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/187/1/psrr05-2005.pdf
Hughes, Gillian and Subba Rao, T (2006) Statistical Analysis and Time Series Models for Minimum/Maximum Temperatures in the Antarctic Peninsula. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:188
2017-11-08T18:18:29Z
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https://eprints.maths.manchester.ac.uk/188/
Higher Order Cumulants of Random Vectors
and Applications to Statistical Inference
and Time Series
Rao Jammalamadaka, S
Subba Rao, T
Terdik, Gyorgy
60 Probability theory and stochastic processes
62 Statistics
This paper provides a unified and comprehensive approach that is useful in deriving expressions for higher order cumulants of random vectors. The use of this methodology is then illustrated in three
diverse and novel contexts, namely: (i) in obtaining a lower bound (Bhattacharya bound) for the variance-
covariance matrix of a vector of unbiased estimators where the density depends on several parameters,
(ii) in studying the asymptotic theory of multivariable statistics when the population is not necessarily
Gaussian and finally, (iii) in the study of multivariate nonlinear time series models and in obtaining higher
order cumulant spectra. The approach depends on expanding the characteristic functions and cumulant
generating functions in terms of the Kronecker products of di¤erential operators. Our objective here is
to derive such expressions using only elementary calculus of several variables and also to highlight some
important applications in statistics.
2006-03-21
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/188/1/psrr06-2005.pdf
Rao Jammalamadaka, S and Subba Rao, T and Terdik, Gyorgy (2006) Higher Order Cumulants of Random Vectors and Applications to Statistical Inference and Time Series. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:192
2017-11-08T18:18:29Z
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https://eprints.maths.manchester.ac.uk/192/
Testing Nonstationary Time Series for
Gaussianity and Linearity using
the Evolutionary Bispectrum:
An application to Internet Traffic Data
Subba Rao, T
Tsolaki, E
62 Statistics
We propose statistical tests for Gaussianity and linearity of nonstationary time series based on the evolutionary bispectrum. These tests can be applied to a particular subclass of nonstationary processes, the so-called oscillatory (also known as slowly-varying) processes. We then apply these tests to time series of network measurements arising from internet traffic. Recent works by several researchers have demonstrated that such internet trafic processes are typically nonstationary. Also, the question of whether such processes can be described by some model whose parameters vary with time has been raised and studied at some length. We use the tests developed in this paper to show that there is evidence of non Gaussianity and nonlinearity in such processes uner the assumption that they are described by a model whose parameters (and so its spectral characteristics) vary slowly with time.
2006-03-24
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/192/1/psrr07-2005.pdf
Subba Rao, T and Tsolaki, E (2006) Testing Nonstationary Time Series for Gaussianity and Linearity using the Evolutionary Bispectrum: An application to Internet Traffic Data. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:203
2017-11-08T18:18:29Z
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https://eprints.maths.manchester.ac.uk/203/
On the Spectral Density Estimation of
Periodically Correlated (Cyclostationary)
Time Series
Nematollahi, A. R.
Subba Rao, T.
62 Statistics
We consider the estimation of the spectral density matrix of a periodically
correlated (PC) time series (also known as cyclostationary time series).
We use the well known relation between the spectral density matrix
of a periodically correlated time series and a stationary vector time series
(Gladyshev, 1961). The spectral matrix of the stationary vector time
series is estimated using the eigenvalue decomposition of block Toeplitz
matrices. The method of estimation is illustrated with simulated and real
time series.
2006-03-30
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/203/1/psrr11-2005.pdf
Nematollahi, A. R. and Subba Rao, T. (2006) On the Spectral Density Estimation of Periodically Correlated (Cyclostationary) Time Series. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:213
2017-11-08T18:18:29Z
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https://eprints.maths.manchester.ac.uk/213/
Modelling Heterogeneous Covariances in the
Growth Curve Models
Pan, Jianxin
von Rosen, Dietrich
62 Statistics
The growth curve models (GCM) are widely used in longitudinal studies
and repeated measures. Most existing approaches for statistical inference in the GCM
assume a specific structure on the within-subject covariances, for example, compound
symmetry, AR(1) and unstructured covariances. The specification, however, may select a
suboptimal or even wrong model, which in turn may affect the estimates of regression coef-
¯cients and/or bias standard errors of the estimates. Accordingly, statistical inferences of
the models may be severely influenced by misspecification of covariance structures. Within
the framework of the GCM in this paper we propose a data-driven approach for modelling
the within-subject covariance structures, investigate the effects of misspecification of co-
variance structures on statistical inferences, and study the heterogeneity of covariances
between different treatment groups.
2006-04-12
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/213/1/psrr20-2005.pdf
Pan, Jianxin and von Rosen, Dietrich (2006) Modelling Heterogeneous Covariances in the Growth Curve Models. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:236
2017-10-20T14:12:06Z
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https://eprints.maths.manchester.ac.uk/236/
Modelling of Covariance Structures in
Generalised Estimating Equations for
Longitudinal Data
Ye, Huajun
Pan, Jianxin
62 Statistics
When used for modelling longitudinal data generalised estimating equations specify a
working structure for the within-subject covariance matrices, aiming to produce efficient
parameter estimators. However, misspecification of the working covariance structure may
lead to a large loss of efficiency of the estimators of the mean parameters. In this paper
we propose an approach for joint modelling of the mean and covariance structures of
longitudinal data within the framework of generalised estimating equations. The resulting
estimators for the mean and covariance parameters are shown to be consistent and
asymptotically Normally distributed. Real data analysis and simulation studies show that
the proposed approach yields efficient estimators for both the mean and covariance
parameters.
2006-12
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/236/1/Modelling_of_Covariance.pdf
Ye, Huajun and Pan, Jianxin (2006) Modelling of Covariance Structures in Generalised Estimating Equations for Longitudinal Data. Biometrika, 93. pp. 927-941. ISSN 1749-9097
http://biomet.oxfordjournals.org/cgi/reprint/93/4/927
10.1093/biomet/93.4.927
10.1093/biomet/93.4.927
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:242
2017-11-08T18:18:29Z
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https://eprints.maths.manchester.ac.uk/242/
Multivariate Non-Linear Regression with
Applications: A Frequency Domain Approach
Terdik, G
Subba Rao, T
Rao Jammalamadaka, S
62 Statistics
In this paper we consider estimating the parameters of a multivariate multiple nonlinear regression
model with correlated errors, through the use of Finite Fourier Transforms. Consistency and asymp-
totic normality of the weighted least squares estimates are established under various conditions on
the regressor variables. These conditions involve different types of scalings, and such scaling factors
are obtained explicitly for various nonlinear regression models including an interesting model which
requires estimating the frequencies. This is a very classical problem in signal processing and is also
of great interest in many other areas. We illustrate our techniques on the time-series data of polar
motion (which is now widely known as "Chandlers Wobble") where one has to estimate the drift parameters, the offset parameters and the two periodicities associated with elliptical motion. The data
was first analyzed by Arato, Kolmogorov and Sinai who treat it as bivariate time series data satisfying
a finite order time series model. They estimate the periodicities using the coefficients of the models.
Our analysis shows that the two dominant frequencies are 12 hours and 410 days and that the errors
exhibit some long-range dependence.
2006-05-12
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/242/1/psrr25-2005.pdf
Terdik, G and Subba Rao, T and Rao Jammalamadaka, S (2006) Multivariate Non-Linear Regression with Applications: A Frequency Domain Approach. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:243
2017-11-08T18:18:29Z
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https://eprints.maths.manchester.ac.uk/243/
Large Modelling Conditional Covariance
in the Linear Mixed Model
Pan, Jianxin
MacKenzie, Gilbert
62 Statistics
We provide a data-driven method for modelling the conditional, within
subject, covariance matrix arising in linear mixed models (Laird and Ware, 1982).
Given an agreed structure for the between subject covariance matrix we use a regression equation approach to model the within subject covariance matrix. Using an EM
algorithm we estimate all of the parameters in the model simultaneously and obtain
analytical expressions for the standard errors. By re-analyzing Kenward's (1987) cattle
data, we compare our new model with classical menu-selection-based modelling techniques, demonstrating its superiority using the Bayesian Information Criterion (BIC).
We also conduct a simulation study which confirms our observational findings. The paper extends our previous covariance modelling work (Pan and MacKenzie, 2003, 2006)
to the conditional covariance space of the linear mixed model (LMM).
2006-05-12
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/243/1/psrr01-2006.pdf
Pan, Jianxin and MacKenzie, Gilbert (2006) Large Modelling Conditional Covariance in the Linear Mixed Model. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:391
2017-10-20T14:12:11Z
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https://eprints.maths.manchester.ac.uk/391/
Cross-Subtype T-Cell Immune Responses Induced by a Human
Immunodeficiency Virus Type 1 Group M Consensus
Env Immunogen
Weaver, Eric A.
Lu, Zhongjing
Camacho, Zenadio T.
Moukdar, Fatiha
Liao, Hua-Xin
Ma, Ben-Jiang
Muldoon, Mark
Theiler, James
Nabel, Gary J.
Letvin, Norman L.
Korber, Bette T.
Hahn, Beatrice H.
Haynes, Barton F.
Gao, Feng
62 Statistics
92 Biology and other natural sciences
The genetic diversity among globally circulating human immunodeficiency virus type 1 (HIV-1) strains is a
serious challenge for HIV-1 vaccine design. We have generated a synthetic group M consensus env gene (CON6)
for induction of cross-subtype immune responses and report here a comparative study of T-cell responses to
this and natural strain env immunogens in a murine model. Three different strains of mice were immunized
with CON6 as well as subtype A, B, or C env immunogens, using a DNA prime-recombinant vaccinia virus boost
strategy. T-cell epitopes were mapped by gamma interferon enzyme-linked immunospot analysis using five
overlapping Env peptide sets from heterologous subtype A, B, and C viruses. The CON6-derived vaccine was
immunogenic and induced a greater number of T-cell epitope responses than any single wild-type subtype A,
B, and C env immunogen and similar T-cell responses to a polyvalent vaccine. The responses were comparable
to within-clade responses but significantly more than between-clade responses. The magnitude of the T-cell
responses induced by CON6 (measured by individual epitope peptides) was also greater than the magnitude
of responses induced by individual wild-type env immunogens. Though the limited major histocompatibility
complex repertoire in inbred mice does not necessarily predict responses in nonhuman primates and humans,
these results suggest that synthetic centralized env immunogens represent a promising approach for HIV-1
vaccine design that merits further characterization.
2006-07
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/391/2/Weaver_CON6.pdf
other
en
https://eprints.maths.manchester.ac.uk/391/3/updated_supplemental_materials.ppt
other
en
https://eprints.maths.manchester.ac.uk/391/4/supplemental_figure_legends.doc
Weaver, Eric A. and Lu, Zhongjing and Camacho, Zenadio T. and Moukdar, Fatiha and Liao, Hua-Xin and Ma, Ben-Jiang and Muldoon, Mark and Theiler, James and Nabel, Gary J. and Letvin, Norman L. and Korber, Bette T. and Hahn, Beatrice H. and Haynes, Barton F. and Gao, Feng (2006) Cross-Subtype T-Cell Immune Responses Induced by a Human Immunodeficiency Virus Type 1 Group M Consensus Env Immunogen. Journal of Virology, 80 (14). pp. 6745-6756. ISSN 0022-538X
10.1128/JVI.02484-05
10.1128/JVI.02484-05
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:400
2017-10-20T14:12:12Z
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On the asymptotic properties of multivariate sample autocovariances
Boshnakov, Georgi N.
60 Probability theory and stochastic processes
62 Statistics
We show that if a process can be obtained by filtering an autoregressive process, then the asymptotic distribution of sample autocovariances of the former is the same as the asymptotic distribution of linear combinations of sample autocovariances of the latter. This result is used to show that for small lags the sample autocovariances of the filtered process have the same asymptotic distribution as estimators utilizing more information (observations on the associated autoregression process and knowledge of the parameters of the filter). In particular, for a Gaussian ARMA process the first few sample autocovariances are jointly asymptotically efficient.
2005
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/400/1/sdarticle.pdf
Boshnakov, Georgi N. (2005) On the asymptotic properties of multivariate sample autocovariances. Journal of Multivariate Analysis, 92 (1). pp. 42-52. ISSN 0047-259X
http://www.sciencedirect.com/science?_ob=IssueURL&_tockey=%23TOC%236901%232005%23999079998%23525128%23FLA%23&_auth=y&view=c&_acct=C000010021&_version=1&_urlVersion=0&_userid=121749&md5=c3fd579f5f69bdc67a99454e5e386434
10.1016/j.jmva.2003.10.005
10.1016/j.jmva.2003.10.005
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:402
2017-10-20T14:12:12Z
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https://eprints.maths.manchester.ac.uk/402/
Multi-companion matrices
Boshnakov, Georgi N.
60 Probability theory and stochastic processes
62 Statistics
In this paper, we introduce and study the class of multi-companion matrices. They generalize companion matrices in various ways and possess a number of interesting properties. We find explicit expressions for the generalized eigenvectors of multi-companion matrices such that each generalized eigenvector depends on the corresponding eigenvalue and a number of quantities which are functionally independent of the eigenvalues of the matrix and (up to a uniqueness constraint) of each other. Moreover, we obtain a parameterization of a multi-companion matrix through the eigenvalues and these additional quantities. The number of parameters in this parameterization is equal to the number of non-trivial elements of the multi-companion matrix. The results can be applied to statistical estimation, simulation and theoretical studies of periodically correlated and multivariate time series in both discrete- and continuous-time.
2002
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/402/1/Multi-Companion.pdf
Boshnakov, Georgi N. (2002) Multi-companion matrices. Linear Algebra and its Applications, 354 (1-3). p. 53. ISSN 0024-3795
http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=5653&_auth=y&_acct=C000010021&_version=1&_urlVersion=0&_userid=121749&md5=c0ac6650e12358bff7a7401e7ea008fd&chunk=360#360
10.1016/S0024-3795(01)00475-X
10.1016/S0024-3795(01)00475-X
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:403
2017-10-20T14:12:12Z
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https://eprints.maths.manchester.ac.uk/403/
Confidence characteristics of distributions
Boshnakov, Georgi N.
60 Probability theory and stochastic processes
62 Statistics
We introduce the confidence characteristic of a distribution as the distribution corresponding to the decomposition concentration function. We show that the decomposition concentration function has very good differentiability properties for any distribution, that the Lebesgue measures of the shortest confidence regions of a distribution and its confidence characteristic are the same, and that similar properties hold for the entropies and the level sets of their densities.
2003
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/403/1/Confidence_Characteristics.pdf
Boshnakov, Georgi N. (2003) Confidence characteristics of distributions. Statistics and Probability Letters, 63 (4). pp. 353-360. ISSN 0167-7152
http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=5672&_auth=y&_acct=C000010021&_version=1&_urlVersion=0&_userid=121749&md5=758778fd84a4f95279732aaf144bae33&chunk=70#70
10.1016/S0167-7152(03)00100-7
10.1016/S0167-7152(03)00100-7
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:404
2017-10-20T14:12:12Z
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https://eprints.maths.manchester.ac.uk/404/
On Some Concepts of Residuals
Boshnakov, Georgi N.
60 Probability theory and stochastic processes
62 Statistics
We introduce confidence residuals and standardised confidence residuals. These residuals may be especially useful for asymmetric and multimodal distributions.
2004
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/404/1/Residuals.pdf
Boshnakov, Georgi N. (2004) On Some Concepts of Residuals. Pliska Studia Mathematica Bulgarica, 16. pp. 23-33. ISSN 0204-9805
http://www.math.bas.bg/~pliska/vol16_04.html#bosh1
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:416
2017-11-08T18:18:29Z
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https://eprints.maths.manchester.ac.uk/416/
Identification of Vessels from Engine Sounds by Spectral Comparison and Verification
Yuan, Jingsong
62 Statistics
We consider the problem of identifying a vessel from its engine sound. A database of known vessels is used for comparison of acoustic characteristics in the frequency domain. Only one training sample is required from each class for classification. With more training samples, a vessel is not only classified but also verified whether it belongs to the same class as its closest match in the database. The acoustic signals are regarded as stationary time series with mixed spectra. We boost their power by adding a small amount of noise in order to assist classification. Three nonparametric estimators of spectra
are compared in classification and verification experiments. The case of a vessel not being represented in the database is also considered with the intention to have it rejected at the verification stage.
2006-07-27
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/416/1/sounds.pdf
Yuan, Jingsong (2006) Identification of Vessels from Engine Sounds by Spectral Comparison and Verification. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:524
2017-10-20T14:12:16Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3630
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/524/
On modelling mean-covariance structures in longitudinal studies
Pan, Jianxin
Mackenzie, Gilbert
60 Probability theory and stochastic processes
62 Statistics
We exploit a reparameterisation of the marginal covariance matrix arising in longitudinal studies (Pourahmadi, 1999, 2000) to model, jointly, the mean and covariance structures in terms of three polynomial functions of time.By reanalysing Kenward's (1987) cattle data, we compare model selection procedures based on regressogram estimation with these based on a global search of the model space. Using a BIC-based model selection criterion to identify the optimum degree triple of the three polynomials, we show that the use of a saturated mean model is not optimal and explain why regressogram-based model estimation may be misleading. We also suggest a new computational method for finding the global optimum based on a criterion involving three pairwise saturated profile likelihoods.
2003
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/524/1/239.pdf
Pan, Jianxin and Mackenzie, Gilbert (2003) On modelling mean-covariance structures in longitudinal studies. Biometrika, 90 (1). pp. 239-244. ISSN 0006-3444
http://biomet.oxfordjournals.org/cgi/content/abstract/90/1/239
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:525
2017-10-20T14:12:16Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
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https://eprints.maths.manchester.ac.uk/525/
On hypotheses testing for the selection of the spatio-temporal models
Antunes, Ana Mónica C.
Subba Rao, Tata
62 Statistics
Several models have been proposed in recent years for analysing spatial data and also, to some extent, spatio-temporal data. One of the important problems, namely the choice of an appropriate model for describing real data sets, remains unsolved. Here we consider the analysis of spatio-temporal processes from which observations over space and time are available. We propose statistical tests for discriminating between space-time autoregressive processes and multivariate autoregressive processes. The sampling properties of the proposed tests are considered. We illustrate the methods with a real example. We use the above tests to find the best model to describe spatio-temporal variations of hourly carbon monoxide measurements at four locations in London in January 2004.
2006
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/525/1/On_Hypotheses.pdf
Antunes, Ana Mónica C. and Subba Rao, Tata (2006) On hypotheses testing for the selection of the spatio-temporal models. Journal of Time Series Analysis, 27 (5). pp. 767-791. ISSN 0143-9782
http://www.ingentaconnect.com/content/bpl/jtsa/2006/00000027/00000005/art00008
10.1111/j.1467-9892.2006.00488.x
10.1111/j.1467-9892.2006.00488.x
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:550
2017-10-20T14:12:17Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
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https://eprints.maths.manchester.ac.uk/550/
The great circle epidemic model
Ball, Frank
Neal, Peter
62 Statistics
We consider a stochastic model for the spread of an epidemic among a population of n individuals that are equally spaced around a circle. Throughout its infectious period, a typical infective, i say, makes global contacts, with individuals chosen independently and uniformly from the whole population, and local contacts, with individuals chosen independently and uniformly according to a contact distribution centred on i. The asymptotic situation in which the local contact distribution converges weakly as n→∞ is analysed. A branching process approximation for the early stages of an epidemic is described and made rigorous as n→∞ by using a coupling argument, yielding a threshold theorem for the model. A central limit theorem is derived for the final outcome of epidemics that take off, by using an embedding representation. The results are specialised to the case of a symmetric, nearest-neighbour local contact distribution.
2003
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/550/1/sdarticle1.pdf
Ball, Frank and Neal, Peter (2003) The great circle epidemic model. Stochastic Processes and their Applications, 107 (2). pp. 233-268. ISSN 0304-4149
http://www.sciencedirect.com/science?_ob=IssueURL&_tockey=%23TOC%235670%232003%23998929997%23449951%23FLA%23&_auth=y&view=c&_acct=C000010021&_version=1&_urlVersion=0&_userid=121749&md5=09a7a8ad9b5650ab16fb0a2efd37411a
10.1016/S0304-4149(03)00074-7
10.1016/S0304-4149(03)00074-7
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:561
2017-10-20T14:12:17Z
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https://eprints.maths.manchester.ac.uk/561/
Growth Curve Models and Statistical Diagnostics
Pan, Jianxin
Fang, Kai-Tai
62 Statistics
Growth-curve models are generalized multivariate analysis-of-variance models. The basic idea of the models is to use different polynomials to fit different treatment groups involved in the longitudinal study. It is not uncommon, however, to find outliers and influential observations in growth data that heavily affect statistical inference in growth curve models. This book provides a comprehensive introduction to the theory of growth curve models with an emphasis on statistical diagnostics. A variety of issues on model fittings and model diagnostics are addressed, and many criteria for outlier detection and influential observation identification are created within likelihood and Bayesian frameworks. This book is intended for postgraduates and statisticians whose research involves longitudinal study, multivariate analysis and statistical diagnostics, and also for scientists who analyze longitudinal data and repeated measures. The authors provide theoretical details on the model fittings and also emphasize the application of growth curve models to practical data analysis, which are reflected in the analysis of practical examples given in each chapter. The book assumes a basic knowledge of matrix algebra and linear regression. Jian-Xin Pan is a lecturer in Medical Statistics of Keele University in the U.K. He has published more than twenty papers on growth curve models, statistical diagnostics and linear/non-linear mixed models. He has a long-standing research interest in longitudinal data analysis and repeated measures in medicine and agriculture. Kai-Tai Fang is a chair professor in Statistics of Hong Kong Baptist University and a fellow of the Institute of Mathematical Statistics. He has published several books with Springer-Verlag, Chapman & Hall, and Science Press and is an author or co-author of over one hundred papers. His research interest includes generalized multivariate analysis, elliptically contoured distributions and uniform design.
Springer
2002
Book
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/561/1/Growth_Curve.pdf
Pan, Jianxin and Fang, Kai-Tai (2002) Growth Curve Models and Statistical Diagnostics. Springer Series in Statistics . Springer, London. ISBN 0-387-95053-2
http://www.amazon.com/gp/product/0387950532
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:563
2017-10-20T14:12:18Z
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https://eprints.maths.manchester.ac.uk/563/
Regression models for covariance structures in longitudinal studies
Pan, Jianxin
MacKenzie, Gilbert
62 Statistics
A convenient reparametrization of the marginal covariance matrix arising in longitudinal studies is discussed. The new parameters have transparent statistical interpretations, are unconstrained and may be modelled parsimoniously in terms of polynomials of time. We exploit this framework to model the dependence of the covariance structure on baseline covariates, time and their interaction. The rationale is based on the assumption that a homogeneous covariance structure with respect to the covariate space is a testable model choice. Accordingly, we provide methods for testing this assumption by incorporating covariates along with time into the model for the covariance structure. We also present new computational algorithms which can handle unbalanced longitudinal data, thereby extending existing methods. The new model is used to analyse Kenward's (1987) cattle data, and the findings are compared with published analyses of the same data set.
2006
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/563/1/Regression.pdf
Pan, Jianxin and MacKenzie, Gilbert (2006) Regression models for covariance structures in longitudinal studies. Statistical Modelling, 6 (1). pp. 43-57. ISSN 1471-082x
http://www.ingentaconnect.com/search/article?title=Regression+Models&title_type=title&author=Pan&journal=1471-082X&journal_type=issn&volume=6&issue=1&year_from=1998&year_to=2006&database=1&pageSize=20&index=1
10.1191/1471082X06st105oa
10.1191/1471082X06st105oa
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:578
2017-10-20T14:12:18Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
7375626A656374733D4D5343:4D53435F3932
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https://eprints.maths.manchester.ac.uk/578/
Computational approahes to parameter estimation and model selection in immunology
Baker, C. T. H.
Bocharov, G. A.
Ford, J. M.
Lumb, P. M.
Norton, S. J.
Paul, C. A. H.
Junt, T.
Krebs, P.
Ludewig, B.
62 Statistics
92 Biology and other natural sciences
One of the significant challenges in biomathematics (and other areas of science) is to formulate meaningful mathematical models. Our problem is to decide on a parametrized model which is, in some sense, most likely to represent the information in a set of observed data. In this paper, we illustrate the computational implementation of an information-theoretic approach (associated with a maximum likelihood treatment) to modelling in immunology.
The approach is illustrated by modelling LCMV infection using a family of models based on systems of ordinary differential and delay differential equations. The models (which use parameters that have a scientific interpretation) are chosen to fit data arising from experimental studies of virus-cytotoxic T lymphocyte kinetics; the parametrized models that result are arranged in a hierarchy by the computation of Akaike indices. The practical illustration is used to convey more general insight. Because the mathematical equations that comprise the models are solved numerically, the accuracy in the computation has a bearing on the outcome, and we address this and other practical details in our discussion.
2005
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/578/1/sdarticle1.pdf
Baker, C. T. H. and Bocharov, G. A. and Ford, J. M. and Lumb, P. M. and Norton, S. J. and Paul, C. A. H. and Junt, T. and Krebs, P. and Ludewig, B. (2005) Computational approahes to parameter estimation and model selection in immunology. Journal of Computational and Applied Mathematics, 184 (1). pp. 50-76. ISSN 0377-0427
http://www.sciencedirect.com/science?_ob=PublicationURL&_tockey=%23TOC%235619%232005%23998159998%23603781%23FLA%23&_cdi=5619&_pubType=J&_auth=y&_acct=C000010021&_version=1&_urlVersion=0&_userid=121749&md5=85d537d318e6369850e6d41dd240c608
10.1016/j.cam.2005.02.003
10.1016/j.cam.2005.02.003
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:585
2017-11-08T18:18:29Z
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https://eprints.maths.manchester.ac.uk/585/
Singular value decomposition of multi-companion matrices
Boshnakov, Georgi
15 Linear and multilinear algebra; matrix theory
62 Statistics
We obtain the singular value decomposition of multi-companion matrices. We completely
characterise the columns of the matrix $U$ and give a simple formula for obtaining the
columns of the other unitary matrix, $V$, from the columns of $U$. We also obtain necessary
and sufficient conditions for the related matrix polynomial to be hyperbolic.
2006-09-04
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/585/1/mcsvd.pdf
Boshnakov, Georgi (2006) Singular value decomposition of multi-companion matrices. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:650
2017-10-20T14:12:21Z
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7375626A656374733D4D5343:4D53435F3638
7375626A656374733D4D5343:4D53435F3932
74797065733D746865736973
https://eprints.maths.manchester.ac.uk/650/
Microarray Data Analysis Using Probabilistic Methods
Liu, Xuejun
62 Statistics
68 Computer science
92 Biology and other natural sciences
Affymetrix microarrays are currently the most widely used microarray technology. Due to the complexity of microarray experiments, the experimental data is very noisy. Many summarization methods have been developed to provide gene expression levels from Affymetrix probe-level data. Most of the currently popular methods do not provide a measure of uncertainty for the estimated expression level of each gene. The use of probabilistic models can overcome this limitation. This thesis extends a previously developed probabilistic model, mgMOS, to obtain an improved model, multi-mgMOS. This new model provides improved accuracy and is more computationally efficient than other alternatives. It also provides a level of uncertainty associated with the measured gene expression level. This probe-level measurement error provides useful information to help in the downstream analysis of gene expression data.
In order to show the advantage of the probe-level probabilistic model, the obtained uncertainty is propagated in two downstream analyses of gene expression data. One is detecting differential gene expression, another is clustering. A Bayesian hierarchical model is proposed to include probe-level measurement error into the detection of differential gene expression from replicated experiments and a standard model-based clustering method is augmented to incorporate probe-level measurement error. Due to the inclusion of the probe-level measurement error, the downstream probabilistic models become more complicated or intractable. In order to perform inference with these augmented models efficiently, various inference approximation approaches are compared in this thesis, including Maximum a Posteriori, Laplace approximation, a variational method and Markov chain Monte Carlo. Results from both benchmark data sets and a real-world data set demonstrate that the incorporation of the probe-level measurement error improves the performance of the downstream probabilistic analysis.
2006-11-10
Thesis
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/650/1/liu_xuejun.pdf
Liu, Xuejun (2006) Microarray Data Analysis Using Probabilistic Methods. Doctoral thesis, The University of Manchester.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:655
2017-11-07T22:38:44Z
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:660
2017-11-08T18:18:30Z
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7375626A656374733D4D5343:4D53435F3632
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https://eprints.maths.manchester.ac.uk/660/
Texture Classification and Verification Using Bispectral Estimates at All the Frequencies on a Lattice
Yuan, Jingsong
62 Statistics
Digitized texture images can often be considered as realisations of stationary
random fields and their estimated normalised bispectra at diagonal frequencies
have been used for classification. In this paper, we devise a classifier and a
hypothesis test using bispectral estimates at all the discrete frequencies
on a lattice. For flexibility textures in each class are allowed to have a certain
amount of variation in theoretical normalised bispectra from that of a single
training sample for the class, and we also consider the case where the texture
to be classified does not belong to any of the classes. The novelty of this
paper is in a) the flexible formulation of the problem,
b) the known asymptotic distribution of the classifier,
c) the inclusion of a verification stage and
d) the complete coverage of frequencies on a lattice.
The methodology is extendable to 4th and higher order spectra and is applicable
to random field data other than texture images.
2006-11-28
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/660/1/bclass.pdf
Yuan, Jingsong (2006) Texture Classification and Verification Using Bispectral Estimates at All the Frequencies on a Lattice. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:665
2017-11-08T18:18:30Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
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https://eprints.maths.manchester.ac.uk/665/
Efficient order
selection algorithms for integer valued ARMA processes
Enciso-Mora, Victor
Neal, Peter
Subba Rao, Tata
62 Statistics
We consider the problem of model (order) selection for integer
valued autoregressive moving-average (INARMA) processes. A very
efficient Reversible Jump Markov chain Monte Carlo (RJMCMC)
algorithm is constructed for moving between INARMA processes of
different order. An alternative in the form of the EM algorithm is
given for determining the order of an integer valued autoregressive
(INAR) process. Both algorithms are successfully applied to both
simulated and real data sets.
2006-12-12
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/665/1/model_051206.pdf
Enciso-Mora, Victor and Neal, Peter and Subba Rao, Tata (2006) Efficient order selection algorithms for integer valued ARMA processes. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:676
2017-11-08T18:18:30Z
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7375626A656374733D4D5343:4D53435F3630
7375626A656374733D4D5343:4D53435F3632
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/676/
Optimal Scaling for Random walk Metropolis on
spherically constrained target densities
Neal, Peter
Roberts, Gareth
60 Probability theory and stochastic processes
62 Statistics
We consider the problem of optimal scaling of the proposal variance
for multidimensional Random walk Metropolis (RWM) algorithms. It is
well known, for a wide range of continuous target densities, that
the optimal scaling of the proposal variance leads to an average
acceptance rate of 0.234. Therefore a natural question is, do
similar results for target densities which have discontinuities? In
the current work, we answer in the affirmative for a class of
spherically constrained target densities. Even though the acceptance
probability is more complicated than for continuous target
densities, the optimal scaling of the proposal variance again leads
to an average acceptance rate of 0.234.
2006-12-20
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/676/1/hypersphere_191206_submit.pdf
Neal, Peter and Roberts, Gareth (2006) Optimal Scaling for Random walk Metropolis on spherically constrained target densities. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:697
2017-10-20T14:12:22Z
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7375626A656374733D4D5343:4D53435F3632
7375626A656374733D4D5343:4D53435F3932
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/697/
Antigenicity and immunogenicity of HIV-1 consensus subtype B
envelope glycoproteins
Kothe, Denise L.
Decker, Julie M.
Li, Yingying
Weng, Zhiping
Bibollet-Ruche, Frederic
Zammit, Kenneth P.
Slazar, Maraia G.
Chen, Yalu
Salazar-Gonzalez, Jesus F.
Moldoveanu, Zina
Mestecky, Jiri
Gao, Feng
Haynes, Barton F.
Shaw, George M.
Muldoon, Mark
Korber, Bette T. M.
Hahn, Beatrice H.
62 Statistics
92 Biology and other natural sciences
“Centralized” (ancestral and consensus) HIV-1 envelope immunogens induce broadly cross-reactive T cell responses in laboratory animals; however, their potential to elicit cross-reactive neutralizing antibodies has not been fully explored. Here, we report the construction of a panel of consensus subtype B (ConB) envelopes and compare their biologic, antigenic, and immunogenic properties to those of two wild-type Env controls from individuals with early and acute HIV-1 infection. Glycoprotein expressed from full-length (gp160), uncleaved (gp160-UNC), truncated (gp145), and N-linked glycosylation site deleted (gp160-201N/S) versions of the ConB env gene were packaged into virions and, except for the fusion defective gp160-UNC, mediated infection via the CCR5 co-receptor. Pseudovirions containing ConB Envs were sensitive to neutralization by patient plasma and monoclonal antibodies, indicating the preservation of neutralizing epitopes found in contemporary subtype B viruses. When used as DNA vaccines in guinea pigs, ConB and wild-type env immunogens induced appreciable binding, but overall only low level neutralizing antibodies. However, all four ConB immunogens were significantly more potent than one wild-type vaccine at eliciting neutralizing antibodies against a panel of tier 1 and tier 2 viruses, and ConB gp145 and gp160 were significantly more potent than both wild-type vaccines at inducing neutralizing antibodies against tier 1 viruses. Thus, consensus subtype B env immunogens appear to be at least as good as, and in some instances better than, wild-type B env immunogens at inducing a neutralizing antibody response, and are amenable to further improvement by specific gene modifications.
2007-03-30
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/697/2/Kothe_Virology360.pdf
Kothe, Denise L. and Decker, Julie M. and Li, Yingying and Weng, Zhiping and Bibollet-Ruche, Frederic and Zammit, Kenneth P. and Slazar, Maraia G. and Chen, Yalu and Salazar-Gonzalez, Jesus F. and Moldoveanu, Zina and Mestecky, Jiri and Gao, Feng and Haynes, Barton F. and Shaw, George M. and Muldoon, Mark and Korber, Bette T. M. and Hahn, Beatrice H. (2007) Antigenicity and immunogenicity of HIV-1 consensus subtype B envelope glycoproteins. Virology, 360 (1). pp. 218-234. ISSN 0042-6822 (In Press)
10.1016/j.virol.2006.10.017
10.1016/j.virol.2006.10.017
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:739
2017-10-20T14:12:24Z
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https://eprints.maths.manchester.ac.uk/739/
Behavioral and physical masculinization are related to genotype in girls with congenital adrenal hyperplasia
Hall, Catherine. M
Jones, Julie. A
Meyer-Bahlburg, Heino. F. L
Dolezal, Curtis
Coleman, Michelle
Foster, Peter
Price, David. A
Clayton, Peter. E
62 Statistics
Royal Manchester Children’s Hospital (C.M.H., J.A.J., D.A.P., P.E.C.), Manchester M27 4HA, Regional Molecular Genetics Laboratory (M.C.), St. Mary’s Hospital, Manchester M13 0JH, and Department of Mathematics (P.F.), University of Manchester, Manchester M13 9PL, United Kingdom; and Department of Psychiatry (H.F.L.M.-B., C.D.), Columbia University, New York, New York 10027
Address all correspondence and requests for reprints to: Catherine M. Hall, Endocrine Department, Royal Manchester Children’s Hospital, Manchester M27 4HA, United Kingdom. E-mail: catherine.hall@cmmc.nhs.uk.
Girls with congenital adrenal hyperplasia (CAH) exhibit behavioral masculinization. There is controversy about the roles of pre- and postnatal androgens, social factors, and chronic illness in its etiology.
To assess the effect of chronic illness, we compared behavioral masculinity in 24 CAH girls and 25 diabetic girls aged 3–12 yr from Manchester using two sensitive questionnaires, and an overall masculinity score M (high = masculine) was derived.
To assess the contributions of pre- and postnatal androgens, the CAH subjects were categorized into genotype groups (G) according to the reported severity of loss of CYP21 function: G1 (n = 10, null mutations), G2 (n = 9, intron 2G), G3 (n = 3, I172N), and G4 (n = 2, unknown loss of function). In CAH girls, relationships between G, Prader degree of genital masculinization at birth, bone age advance, and M were assessed.
CAH girls were less feminine and more masculine than diabetic girls (P < 0.001), who were not significantly different from U.S. controls. Among the CAH girls, those in G1 and 2 were more genitally masculinized than those in G3 and 4 (P < 0.009) and had higher M (P < 0.025). M was negatively correlated with advanced bone age (r = -0.5; P = 0.02).
CAH girls, but not diabetic girls, demonstrated behavioral masculinization. Both physical and behavioral masculinization were related to each other and to genotype, indicating that behavioral masculinization is a consequence of prenatal androgen exposure.
2004
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/739/1/Behavioral_and_Physical.pdf
Hall, Catherine. M and Jones, Julie. A and Meyer-Bahlburg, Heino. F. L and Dolezal, Curtis and Coleman, Michelle and Foster, Peter and Price, David. A and Clayton, Peter. E (2004) Behavioral and physical masculinization are related to genotype in girls with congenital adrenal hyperplasia. Journal of Clinical Endocrinology and Metabolism, 89 (1). pp. 419-424. ISSN 0021-972X
http://jcem.endojournals.org/content/vol89/issue1/
10.1210/jc.2003-030696
10.1210/jc.2003-030696
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:740
2017-10-20T14:12:24Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3333
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/740/
On the ratio X/Y for some elliptically symmetric distributions
Nadarajah, Saralees
33 Special functions (properties of functions as functions)
62 Statistics
The distributions of the ratio X/Y are derived when (X,Y) has the elliptically symmetric Pearson-type II distribution, elliptically symmetric Pearson-type VII distribution and the elliptically symmetric Kotz-type distribution.
2006
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/740/1/On_the_ratio.pdf
Nadarajah, Saralees (2006) On the ratio X/Y for some elliptically symmetric distributions. Journal of Multivariate Analysis, 97 (2). pp. 342-358. ISSN 0047-259X
http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
10.1016/j.jmva.2005.03.004
10.1016/j.jmva.2005.03.004
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:741
2017-10-20T14:12:24Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3333
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/741/
The exponentiated Gumbel distribution with climate application
Nadarajah, Saralees
33 Special functions (properties of functions as functions)
62 Statistics
The Gumbel distribution is perhaps the most widely applied statistical distribution for climate modeling. In this article we introduce a distribution that generalizes the standard Gumbel distribution in the same way the exponentiated exponential distribution generalizes the standard exponential distribution. We refer to this new distribution as the exponentiated Gumbel distribution. We provide a comprehensive treatment of the mathematical properties of this new distribution and illustrate its use for modeling rainfall data from Orlando, Florida. Among the mathematical properties, we derive the analytical shapes of the corresponding probability density function and the hazard rate function, calculate expressions for the nth moment and the asymptotic distribution of the extreme order statistics, and investigate the variation of the skewness and kurtosis measures. We also discuss estimation by the method of maximum likelihood. Copyright © 2005 John Wiley & Sons, Ltd.
2006
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/741/1/The_exponentiated.pdf
Nadarajah, Saralees (2006) The exponentiated Gumbel distribution with climate application. Environmetrics, 17 (1). pp. 13-23. ISSN 1180-4009
http://www3.interscience.wiley.com/cgi-bin/jissue/112217585
10.1002/env.739
10.1002/env.739
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:749
2017-10-20T14:12:24Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/749/
Suppression of puberty with long-acting goserelin (zoladex-LA): effect on gonadotrophin response to GnRH in the first treatment cycle
Trueman, Julie A.
Tillmann, Vallo
Cusick, Colin F.
Foster, Peter
Patel, Leena
Hall, Catherine M.
Price, David A.
Clayton, Peter E.
62 Statistics
background and objectivesDepot GnRH analogues are widely used in the treatment of precocious puberty, or suppression of relatively early puberty where growth or psychosocial well-being may be compromised. One example is Zoladex (Z goserelin 3·6 mg), which can be given every 4 weeks. This injection frequency may not always achieve adequate suppression of pubertal signs. A long-acting form, Zoladex-LA 10·8 mg, has now been introduced with a potential duration of action of 12 weeks. In order to assess the efficacy of Zoladex-LA in gonadotrophin suppression we have measured LH and FSH responses to GnRH at diagnosis and 8 and 12 weeks after injection in a group of children treated with Zoladex-LA for central precocious or early puberty.
methodsForty-nine children (40 girls) with clinical evidence of central precocious puberty (CPP) or early puberty (EP) were started on Zoladex-LA, either de novo (n = 29) or on changing from Zoladex. Ages at diagnosis ranged from 1·7 to 10·6 years (median 7·8 years). Twenty-three had a structural cause with abnormality on magnetic resonance/computerized tomography (MR/CT) head scan, nine had a syndrome or nonspecific brain injury, and in 17 the cause was idiopathic.
resultsAt diagnosis, in the de novo group, median peak LH was 13·6 IU/l and median peak FSH was 12·0 IU/l. By 12 weeks gonadotrophins were suppressed to 0·9 and 0·8 IU/l, respectively. In the previously treated group, median peak LH at diagnosis was 12·8 IU/l and median peak FSH was 15·0 IU/l with suppression to 0·8 and 1·1 IU/l, respectively, at 12 weeks. In the latter group peak FSH was higher than peak LH at both 8 and 12 weeks (P < 0·05) and there was a significant rise in peak LH (P < 0·05) and FSH (P = 0·01) between 8 and 12 weeks. There was no correlation between age at diagnosis and peak LH or FSH at 8 or 12 weeks. Nevertheless, individual patients in both groups showed evidence of incomplete gonadotrophin suppression at 12 weeks.
conclusionZoladex-LA induces a significant reduction in gonadotrophins over 12 weeks. However, there are individuals, particularly those previously on Zoladex, in whom gonadotrophin suppression is waning by 12 weeks. As found with Zoladex, some children with precocious puberty treated with Zoladex-LA may require increased injection frequency, although correlation with clinical evidence of suppression needs to be studied further.
2002
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/749/1/Suppression.pdf
Trueman, Julie A. and Tillmann, Vallo and Cusick, Colin F. and Foster, Peter and Patel, Leena and Hall, Catherine M. and Price, David A. and Clayton, Peter E. (2002) Suppression of puberty with long-acting goserelin (zoladex-LA): effect on gonadotrophin response to GnRH in the first treatment cycle. Clinical Endocrinology, 57 (2). pp. 223-230. ISSN 0300-0664
http://www.blackwell-synergy.com/doi/abs/10.1046/j.1365-2265.2002.01571.x
10.1046/j.1365-2265.2002.01571.x
10.1046/j.1365-2265.2002.01571.x
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:750
2017-10-20T14:12:24Z
7374617475733D707562
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https://eprints.maths.manchester.ac.uk/750/
Short-term growth in children with growth disorders
Tillmann, V.
Foster, P. J.
Gill, M. S.
Rice, D. A. P.
Clayton, P. E.
62 Statistics
Objective : We have previously demonstrated that normal prepubertal growth over 1 year is composed of growth spurts lasting an average of 8 weeks, separated by periods of very slow growth or stasis. We have now analysed short-term growth patterns in eight children with different growth disorders: Turner syndrome ( n = 2), intrauterine growth retardation (IUGR, n = 1) and growth hormone (GH) deficiency (GHD, n = 5).
Methodology : Height was measured daily in the morning by parents over 4-12 months. Regression and time series analysis were used to characterize short-term growth. In two boys (GHD and IUGR) their normal twin brother was measured in parallel.
Results : All height velocity curves, based on regression analysis, showed a biphasic pattern, characterized by growth spurts of varying amplitudes and periods of very slow growth or growth stasis. When compared to growth curves in normal children, the principal qualitative differences in GHD and Turner syndrome were increased stasis time and reduced growth spurt amplitude. In IUGR reduced amplitude and length of growth spurts were seen, but the time spent in stasis was similar to normal children. Two naive patients with GHD increased the amplitude of their growth spurts by a mean 0.013 cm day -1 on GH treatment, with the mean length of their growth spurts increasing by 10 days. Their time spent in stasis decreased from 19% to 6% on GH. In two subjects with GHD the growth pattern during maintenance GH treatment was similar to that seen in normal children. Using time series analysis significant periodicities in height measurements were seen in the majority of children with growth disorders, which disappeared in patients with GHD in the catch-up phase after commencing GH therapy.
Conclusions : (1) The growth spurts and stases seen in normal children are also observed in those with growth disorders, (2) different growth disorders have variable effects on the spurt-stasis model of childhood growth, (3) catch-up growth on GH in children with GHD was achieved by increasing the amplitude of the growth spurts and reducing the time spent in stasis.
2002
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/750/1/Short-term_growth.pdf
Tillmann, V. and Foster, P. J. and Gill, M. S. and Rice, D. A. P. and Clayton, P. E. (2002) Short-term growth in children with growth disorders. Annals of Human Biology, 29 (1). pp. 89-104. ISSN 0301-4460
http://www.informaworld.com/smpp/content~content=a713801556~db=all~order=page
10.1080/03014460110075666
10.1080/03014460110075666
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:785
2017-11-08T23:32:08Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3533
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/785/
Universal connection and curvature for statistical manifold geometry
Arwini, Khadiga
Del Riego, L
Dodson, CTJ
53 Differential geometry
62 Statistics
Statistical manifolds are representations of smooth families of
probability density functions
that allow differential geometric methods to be applied to
problems in stochastic processes, mathematical statistics and
information theory. It is common to have to consider a number of
linear connections on a given statistical manifold and so it is
important to know the corresponding universal connection and
curvature; then all linear connections and their curvatures are
pullbacks. An important class of statistical manifolds is that
arising from the exponential families and one particular family is
that of gamma distributions, which we showed recently to have
important uniqueness properties in stochastic processes. Here we
provide formulae for universal connections and curvatures on
exponential families and give an explicit example for the manifold
of gamma distributions.
2007
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/785/1/univconexpf.pdf
Arwini, Khadiga and Del Riego, L and Dodson, CTJ (2007) Universal connection and curvature for statistical manifold geometry. Houston Journal of Mathematics, 33 (1). pp. 145-161. ISSN 0362-1588
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:815
2017-11-08T23:32:08Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3533
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/815/
Universal connection and curvature for statistical manifold geometry
Arwini, Khadiga
Del Riego, L
Dodson, CTJ
53 Differential geometry
62 Statistics
Statistical manifolds are representations of smooth families of
probability density functions
that allow differential geometric methods to be applied to
problems in stochastic processes, mathematical statistics and
information theory. It is common to have to consider a number of
linear connections on a given statistical manifold and so it is
important to know the corresponding universal connection and
curvature; then all linear connections and their curvatures are
pullbacks. An important class of statistical manifolds is that
arising from the exponential families and one particular family is
that of gamma distributions, which we showed recently to have
important uniqueness properties in stochastic processes. Here we
provide formulae for universal connections and curvatures on
exponential families and give an explicit example for the manifold
of gamma distributions.
2007
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/815/1/univconexpf.pdf
Arwini, Khadiga and Del Riego, L and Dodson, CTJ (2007) Universal connection and curvature for statistical manifold geometry. Houston Journal of Mathematics, 33 (1). pp. 145-162. ISSN 0362-1588
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:822
2017-11-08T18:18:30Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3630
7375626A656374733D4D5343:4D53435F3632
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/822/
Optimal Scaling for Random walk Metropolis on
spherically constrained target densities
Neal, Peter
Roberts, Gareth
60 Probability theory and stochastic processes
62 Statistics
We consider the problem of optimal scaling of the proposal variance
for multidimensional Random walk Metropolis (RWM) algorithms. It is
well known, for a wide range of continuous target densities, that
the optimal scaling of the proposal variance leads to an average
acceptance rate of 0.234. Therefore a natural question is, do
similar results for target densities which have discontinuities? In
the current work, we answer in the affirmative for a class of
spherically constrained target densities. Even though the acceptance
probability is more complicated than for continuous target
densities, the optimal scaling of the proposal variance again leads
to an average acceptance rate of 0.234.
2007-07-09
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/822/1/hypersphere_210607_revision.pdf
Neal, Peter and Roberts, Gareth (2007) Optimal Scaling for Random walk Metropolis on spherically constrained target densities. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:835
2017-11-08T18:18:30Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
7375626A656374733D4D5343:4D53435F3932
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/835/
Llama: an online microarray linear analysis tool
Routley, Ben
Muldoon, Mark R.
62 Statistics
92 Biology and other natural sciences
We have developed a linear modelling tool for analysis of two-colour microarray data that utilises a per-spot linear model to estimate expression differences. Given the design of the experiment, the program combines all relevant data to provide the best estimate of a particular difference in expression between samples. It constructs multiple estimates based on several slides and combines them to get the most precise overall estimates of differential expression. Every effort has been made to make this tool accessible to biologists and it contains many user-friendly options
2007-08-23
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/835/1/ApplicationNotev6.pdf
Routley, Ben and Muldoon, Mark R. (2007) Llama: an online microarray linear analysis tool. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:836
2017-11-08T18:18:30Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
7375626A656374733D4D5343:4D53435F3932
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/836/
Review: Practical Design and Analysis of 2-Colour
cDNA Microarray Experiments
Routley, Ben
Muldoon, Mark R.
62 Statistics
92 Biology and other natural sciences
This review paper, is aimed at biological researchers who are interested in or have begun to use cDNA microarrays for their investigations. Large microarray studies typically involve a multi-disciplinary team with various groups performing different aspects of the same experiment. This approach means that microarrays are less accessible to new researchers than more traditional biological techniques. This review aims to make current techniques of statistical design, normalisation and linear analysis of cDNA microarray experiments accessible to a wider community. These methods will be illustrated with examples that use freely-available packages implemented in Bioconductor and R.
2007-08-23
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/836/1/Prac_Des_19_Aug_05.pdf
Routley, Ben and Muldoon, Mark R. (2007) Review: Practical Design and Analysis of 2-Colour cDNA Microarray Experiments. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:896
2017-10-20T14:12:30Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3630
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/896/
Planar line processes for void and density statistics in thin stochastic fibre networks
Dodson, CTJ
Sampson, WW
60 Probability theory and stochastic processes
62 Statistics
Using results for the distribution of perimeters of random polygons arising from random lines in a plane, we obtain new analytic approximations to the distributions of areas and local line densities for random polygons and compute various limiting properties of random polygons. Using simulation, we show that the lengths of adjacent sides of polygons generated by random line processes in the plane are correlated with ρ=0.616±0.001.
2007
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/896/1/PLPJStatistPhys.pdf
Dodson, CTJ and Sampson, WW (2007) Planar line processes for void and density statistics in thin stochastic fibre networks. Journal of Statistical Physics, 129. pp. 311-322. ISSN 0022-4715
http://www.springerlink.com/content/4356q88w62542652/
10.1007/s10955-007-9379-9
10.1007/s10955-007-9379-9
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:897
2017-10-20T14:12:30Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/897/
Some measures for asymmetry of distributions
Boshnakov, Georgi N.
62 Statistics
We propose several measures, functional and scalar, for asymmetry of distributions by comparing the behavior of probability densities to the right and left of the mode(s) and show how to generate classes of equivalent distributions from a given distribution, allowing for varying asymmetry but retaining some information theoretic properties of the original distribution, such as the entropy.
2007
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/897/1/Some_Measures.pdf
Boshnakov, Georgi N. (2007) Some measures for asymmetry of distributions. Statistics and Probability Letters, 77 (11). pp. 1111-1116. ISSN 0167-7152
http://www.sciencedirect.com/science/journal/01677152
10.1016/j.spl.2007.02.002
10.1016/j.spl.2007.02.002
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:898
2017-10-20T14:12:30Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/898/
Design of experiments in the presence of errors in factor levels
Donev, A.N.
62 Statistics
This paper is concerned with the statistical properties of experimental designs where the factor levels cannot be set precisely. When the errors in setting the factor levels cannot be measured, design robustness is explored. However, when the actual design could be measured at the end of the investigation, its optimality is of interest. D-optimality could be assessed in different ways. Several measures are compared. Evaluating them is difficult even in simple cases. Therefore, in general, simulations are used to obtain their values. It is shown that if D-optimality is measured by the expected value of the determinant of the information matrix of the experimental design, as has been suggested in the past, on average the designs appear to improve with the variance of the error in setting the factor levels. However, we argue that the criterion of D-optimality should be based on the inverse of the information matrix. In this case it is shown that the experiment could be better or worse than the planned one. It is also recognized that setting the factor levels with error could lead to an increased risk of losing observations, which on its own could reduce considerably the optimality of the experimental designs. Advice on choosing the design region in such a way that such a risk is controlled to an acceptable level is given.
2003
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/898/1/Design_Of.pdf
Donev, A.N. (2003) Design of experiments in the presence of errors in factor levels. Journal of Statistical Planning and Inference, 126 (2). pp. 569-585. ISSN 0378-3758
http://www.elsevier.com/wps/find/journaldescription.cws_home/505561/description#description
10.1016/j.jspi.2003.09.002
10.1016/j.jspi.2003.09.002
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:899
2017-10-20T14:12:30Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/899/
Blocking response surface designs
Goos, P.
Donev, A.N.
62 Statistics
The design of experiments involving more than one blocking factor and quantitative explanatory variables is discussed, the focus being on two key aspects of blocked response surface designs: optimality and orthogonality. First, conditions for orthogonally blocked experiments are derived. Next, an algorithmic approach to compute D-optimal designs is presented. Finally, the relationships between design optimality and orthogonality in the context of response surface experiments are discussed in detail.
2005
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/899/1/Blocking_Response.pdf
Goos, P. and Donev, A.N. (2005) Blocking response surface designs. Computational Statistics and Data Analysis, 51 (2). pp. 1075-1088. ISSN 0167-9473
http://www.elsevier.com/wps/find/journaldescription.cws_home/505539/description#description
10.1016/j.csda.2005.11.003
10.1016/j.csda.2005.11.003
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:902
2017-10-20T14:12:30Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/902/
Sampling distributions associated with the multivariate t distribution
Nadarajah, Saralees
Kotz, Samuel
62 Statistics
The known sampling distributions and simulation methods associated
with multivariate t distributions are reviewed. We believe that this
review will serve as an important reference and encourage further
research activities in the area.
2005
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/902/1/Sampling_Distributions.pdf
Nadarajah, Saralees and Kotz, Samuel (2005) Sampling distributions associated with the multivariate t distribution. Statistica Neerlandica, 59 (2). pp. 214-234.
http://www.blackwellpublishing.com/journal.asp?ref=0039-0402&site=1
10.1111/j.1467-9574.2005.00288.x
10.1111/j.1467-9574.2005.00288.x
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:903
2017-10-20T14:12:30Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/903/
Modelling conditional covariance in the linear mixed model
Pan, Jianxin
MacKenzie, Gilbert
62 Statistics
We provide a data-driven method for modelling the conditional, within-subject covariance matrix arising in linear mixed models (Laird and Ware, 1982). Given an agreed structure for the between-subject covariance matrix we use a regression equation approach to model the within-subject covariance matrix. Using an EM algorithm we estimate all of the parameters in the model simultaneously and obtain analytical expressions for the standard errors. By re-analyzing Kenward's (1987) cattle data, we compare our new model with classical menu-selection–based modelling techniques, demonstrating its superiority using the Bayesian Information Criterion. We also conduct a simulation study, which confirms our observational findings. The paper extends our previous covariance modeling work (Pan and MacKenzie, 2003, 2006) to the conditional covariance space of the linear mixed model (LMM).
2007
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/903/1/Modelling_Conditional.pdf
Pan, Jianxin and MacKenzie, Gilbert (2007) Modelling conditional covariance in the linear mixed model. Statistical Modelling: An International Journal, 7 (1). pp. 49-71. ISSN 1477-0342
http://smj.sagepub.com/content/vol7/issue1/
10.1177/1471082X0600700104
10.1177/1471082X0600700104
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:904
2017-10-20T14:12:30Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/904/
Quasi-Monte Carlo estimation in generalized linear mixed models
Pan, Jianxin
Thompson, Robin
62 Statistics
Generalized linear mixed models (GLMMs) are useful for modelling longitudinal and clustered data, but parameter estimation is very challenging because the likelihood may involve high-dimensional integrals that are analytically intractable. Gauss–Hermite quadrature (GHQ) approximation can be applied but is only suitable for low-dimensional random effects. Based on the Quasi-Monte Carlo (QMC) approximation, a heuristic approach is proposed to calculate the maximum likelihood estimates of parameters in the GLMM. The QMC points scattered uniformly on the high-dimensional integration domain are generated to replace the GHQ nodes. Compared to the GHQ approximation, the proposed method has many advantages such as its affordable computation, good approximation and fast convergence. Comparisons to the penalized quasi-likelihood estimation and Gibbs sampling are made using a real dataset and a simulation study. The real dataset is the salamander mating dataset whose modelling involves six 20-dimensional intractable integrals in the likelihood.
2006
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/904/1/Quasi-Monte.pdf
Pan, Jianxin and Thompson, Robin (2006) Quasi-Monte Carlo estimation in generalized linear mixed models. Computational Statistics and Data Analysis, 51 (12). pp. 5765-5775. ISSN 0167-9473
http://www.elsevier.com/wps/find/journaldescription.cws_home/505539/description#description
10.1016/j.csda.2006.10.003
10.1016/j.csda.2006.10.003
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:945
2017-10-20T14:12:32Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/945/
Tailor-made split-plot designs for mixture and process variables
Goos, Peter
Donev, Alex
62 Statistics
The design of efficient small experiments involving mixture variables and process variables is a difficult
problem. An additional complication is that such experiments are often conducted using split-plot designs
and therefore lead to correlated observations. The present article demonstrates how algorithmic search can
be used for constructing efficient tailor-made split-plot mixture-process variable designs, when there may
be constraints on the mixture components. The D-optimality criterion is used as the main design criterion.
The article also shows how to construct efficient split-plot mixture-process variable designs when replication
is required for independently estimating the variance components in the split-plot model. It is argued that
it is better to spread the replications over different points of the design than to concentrate them in the
center.
2007
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/945/1/Tailor-Made.pdf
Goos, Peter and Donev, Alex (2007) Tailor-made split-plot designs for mixture and process variables. Journal of Quality Technology, 39 (4). pp. 326-339. ISSN 0020-0255
http://proquest.umi.com/pqdweb?did=1368173061&sid=1&Fmt=2&clientId=44986&RQT=309&VName=PQD
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:946
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The D-optimal design of blocked experiments with mixture components
Goos, Peter
Donev, Alex
62 Statistics
So far, the optimal design of blocked experiments involving mixture components has received scant
attention in the literature. This paper describes the algorithmic approach to designing such experiments.
For constrained and unconstrained experimental regions, the resulting experimental designs are shown to
be statistically much more efficient than the orthogonally blocked design options presented in the literature.
As an alternative to the algorithmic approach, a simple two-stage procedure to construct highly efficient
blocked mixture experiments for unconstrained design regions in the presence of fixed and/or random blocks
is presented. Finally, the similarities and differences between the design of blocked mixture experiments
and mixture experiments in the presence of qualitative process variables are discussed in detail.
2006
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/946/1/The_D-optimal.pdf
Goos, Peter and Donev, Alex (2006) The D-optimal design of blocked experiments with mixture components. Journal of Quality Technology, 38 (4). pp. 319-332. ISSN 0020-0255
http://www.asq.org/pub/jqt/past/vol38_issue4/index.html
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:952
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https://eprints.maths.manchester.ac.uk/952/
Optimum Experimental Designs, With SAS
Atkinson, Anthony
Donev, Alexander
Tobias, Randall
62 Statistics
Experiments on patients, processes or plants all have random error, making statistical methods essential for their efficient design and analysis. This book presents the theory and methods of optimum experimental design, making them available through the use of SAS programs. Little previous statistical knowledge is assumed. The first part of the book stresses the importance of models in the analysis of data and introduces least squares fitting and simple optimum experimental designs. The second part presents a more detailed discussion of the general theory and of a wide variety of experiments. The book stresses the use of SAS to provide hands-on solutions for the construction of designs in both standard and non-standard situations. The mathematical theory of the designs is developed in parallel with their construction in SAS, so providing motivation for the development of the subject. Many chapters cover self-contained topics drawn from science, engineering and pharmaceutical investigations, such as response surface designs, blocking of experiments, designs for mixture experiments and for nonlinear and generalized linear models. Understanding is aided by the provision of "SAS tasks" after most chapters as well as by more traditional exercises and a fully supported website. The authors are leading experts in key fields and this book is ideal for statisticians and scientists in academia, research and the process and pharmaceutical industries.
Oxford University Press
2007
Book
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/952/1/Donev.pdf
Atkinson, Anthony and Donev, Alexander and Tobias, Randall (2007) Optimum Experimental Designs, With SAS. Oxford statistical Science . Oxford University Press, Oxford. ISBN 13: 978-0-19-929659-0
http://www.oup.com/uk/catalogue/?ci=9780199296590
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1015
2017-11-07T22:38:45Z
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1017
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https://eprints.maths.manchester.ac.uk/1017/
A note on quantum chaology and gamma approximations to eigenvalue spacings
for infinite random matrices
Dodson, CTJ
62 Statistics
81 Quantum theory
Quantum counterparts of certain simple classical systems can exhibit chaotic behaviour
through the statistics of their energy levels. Gamma distributions do not
precisely model the various analytic systems discussed here, but some features may be useful in studies of qualitative generic properties in applications to data from real systems which manifestly seem to exhibit behaviour reminiscent of near-random processes.
We use known bounds on the distribution
function for eigenvalue spacings for the Gaussian orthogonal ensemble (GOE) and show that gamma distributions, which have an important uniqueness property, can yield an approximation similarly good, except near the origin, to that of the widely used Wigner surmise.
This has the advantage that then both the chaotic and non chaotic cases fit in the
information geometric framework of the manifold of gamma distributions, which has been
the subject of recent work on neighbourhoods of randomness for more general stochastic systems.
2008-01-17
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1017/1/QC.pdf
Dodson, CTJ (2008) A note on quantum chaology and gamma approximations to eigenvalue spacings for infinite random matrices. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1050
2017-10-20T14:12:35Z
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74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/1050/
A note on quantum chaology and gamma approximations to eigenvalue spacings
for infinite random matrices
Dodson, CTJ
62 Statistics
81 Quantum theory
Quantum counterparts of certain simple classical systems can exhibit chaotic behaviour
through the statistics of their energy levels and the irregular spectra of chaotic systems are modelled by eigenvalues of infinite random matrices.
We use known bounds on the distribution
function for eigenvalue spacings for the Gaussian orthogonal ensemble (GOE) of infinite random real symmetric matrices and show that gamma distributions, which have an important uniqueness property, can yield an approximation to the GOE distribution. That has
the advantage that then both chaotic and non chaotic cases fit in the
information geometric framework of the manifold of gamma distributions, which has been
the subject of recent work on neighbourhoods of randomness for general stochastic systems.
Additionally, gamma
distributions give approximations, to eigenvalue spacings for the Gaussian unitary ensemble (GUE) of infinite random hermitian matrices and for the Gaussian symplectic ensemble (GSE) of infinite random hermitian matrices with real quaternionic elements, except near the origin. Gamma distributions do not
precisely model the various analytic systems discussed here, but some features may be useful in studies of qualitative generic properties in applications to data from real systems which manifestly seem to exhibit behaviour reminiscent of near-random processes.
2008-01-17
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1050/1/QC.pdf
Dodson, CTJ (2008) A note on quantum chaology and gamma approximations to eigenvalue spacings for infinite random matrices. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1118
2017-10-20T14:12:37Z
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74797065733D636F6E666572656E63655F6974656D
https://eprints.maths.manchester.ac.uk/1118/
A note on quantum chaology and gamma approximations to eigenvalue spacings
for infinite random matrices
Dodson, CTJ
62 Statistics
81 Quantum theory
Quantum counterparts of certain simple classical systems can exhibit chaotic behaviour
through the statistics of their energy levels and the irregular spectra of chaotic systems are modelled by eigenvalues of infinite random matrices.
We use known bounds on the distribution
function for eigenvalue spacings for the Gaussian orthogonal ensemble (GOE) of infinite random real symmetric matrices and show that gamma distributions, which have an important uniqueness property, can yield an approximation to the GOE distribution. That has
the advantage that then both chaotic and non chaotic cases fit in the
information geometric framework of the manifold of gamma distributions, which has been
the subject of recent work on neighbourhoods of randomness for general stochastic systems.
Additionally, gamma
distributions give approximations, to eigenvalue spacings for the Gaussian unitary ensemble (GUE) of infinite random hermitian matrices and for the Gaussian symplectic ensemble (GSE) of infinite random hermitian matrices with real quaternionic elements, except near the origin. Gamma distributions do not
precisely model the various analytic systems discussed here, but some features may be useful in studies of qualitative generic properties in applications to data from real systems which manifestly seem to exhibit behaviour reminiscent of near-random processes.
2008-06-05
Conference or Workshop Item
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1118/1/Dodson-chaos2008Slides.pdf
Dodson, CTJ (2008) A note on quantum chaology and gamma approximations to eigenvalue spacings for infinite random matrices. In: CHAOS 2008, 3-6 June 2008, Charnia, Crete.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1121
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https://eprints.maths.manchester.ac.uk/1121/
The Singular Value Decomposition in Multivariate Statistics
Hammarling, Sven
15 Linear and multilinear algebra; matrix theory
62 Statistics
65 Numerical analysis
Many multivariate techniques in statistics are described in terms of an appropriate sums of squares and cross products matrix, such as a covariance matrix, or a correlation matrix, rather than in terms of the original data matrix. While this is frequently the best way of understanding and analysing a technique, it is not necessarily the most satisfactory approach for implementing the technique computationally. From a numerical point of view, it is usually better to work with the data matrix.
This is a review article aimed at the statistician and mathematician who, while not being expert numerical analysts, would like to gain some understanding of why it is better to work with the data matrix, and of the techniques that allow us to avoid the explicit computation of sums and squares and cross products matrices. To give a focus and to keep the article of moderate length, we concentrate in particular on the use of the singular value decomposition and its application to multiple regression problems. In the final two sections we give a brief discussion of principal components, canonical correlations and the generalized singular value decomposition.
1985-07
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1121/1/SVD-Signum85.pdf
Hammarling, Sven (1985) The Singular Value Decomposition in Multivariate Statistics. ACM Signum Newsletter, 20 (3). pp. 2-25.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1163
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https://eprints.maths.manchester.ac.uk/1163/
Cost-cautious designs for confirmatory bioassay
Donev, Alexander N.
Tobias, Randy
Monadjemi, Farinaz
00 General
62 Statistics
Confirmatory bioassay experiments take place in late stages of the drug discovery processwhen
a small number of compounds have to be compared with respect to their properties. As the
cost of the observations may differ considerably, the design problem is well specified by the
cost of compound used rather than by the number of observations. We show that cost-efficient
designs can be constructed using useful properties of the minimum support designs. These designs
are particularly suited for studies where the parameters of the model to be estimated are
known with high accuracy prior to the experiment, although they prove to be robust against
typical inaccuracies of these values. When the parameters of the model can only be specified
with ranges of values or by a probability distribution, we use a Bayesian criterion of optimality
to construct the required designs. Typically, the number of their support points depends on
the prior knowledge for the model parameters. In all cases we recommend identifying a set of
designs with good statistical properties but different potential costs to choose from.
2008
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1163/1/Donev_et_al_2008.pdf
Donev, Alexander N. and Tobias, Randy and Monadjemi, Farinaz (2008) Cost-cautious designs for confirmatory bioassay. Journal of Statistical Planning and Inference, 138. 3805 -3812. ISSN 0378-3758
10.1016/j.jspi.2008.01.015
10.1016/j.jspi.2008.01.015
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1195
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https://eprints.maths.manchester.ac.uk/1195/
Numerical Linear Algebra in Statistical Computing
Higham, Nicholas J.
Stewart, G. W.
62 Statistics
65 Numerical analysis
Some of the factors to be considered when applying the
techniques of numerical linear algebra to statistical problems
are discussed with reference to three particular examples: the
use of the normal equations in regression problems; the use of
perturbation theory to assess the effects of errors in
regression matrices; and the phenomenon of benign degeneracy, in
which the numerical problem becomes more difficult even as the
associated statistical problem becomes easier.
Oxford University Press
Iserles, A.
Powell, M. J. D.
1987
Book Section
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1195/1/hist87.pdf
Higham, Nicholas J. and Stewart, G. W. (1987) Numerical Linear Algebra in Statistical Computing. In: The State of the Art in Numerical Analysis. Oxford University Press, Oxford, UK, pp. 41-57. ISBN 0-19-853614-3
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1286
2017-11-08T18:18:32Z
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https://eprints.maths.manchester.ac.uk/1286/
Nonparametric Regression of Covariance Structures
in Longitudinal Studies
Pan, Jianxin
Ye, Huajin
Li, Runze
15 Linear and multilinear algebra; matrix theory
62 Statistics
In this paper we propose a nonparametric data-driven approach to model
covariance structures for longitudinal data. Based on a modi¯ed Cholesky decomposition,
the within-subject covariance matrix is decomposed into a unit lower triangular matrix in-
volving generalized autoregressive coe±cients and a diagonal matrix involving innovation
variances. Local polynomial smoothing estimation is proposed to model the nonpara-
metric smoothing functions of the mean, generalized autoregressive coe±cients and (log)
innovation variances, simultaneously. We provide theoretical justi¯cation of consistency of
the ¯tted smoothing curves in the mean, generalized autoregressive parameters and (log)
innovation variances. Two real data sets are analyzed for illustration. Simulation studies
are made to evaluate the e±cacy of the proposed method.
2009-07-09
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1286/1/mlocal28102008.pdf
Pan, Jianxin and Ye, Huajin and Li, Runze (2009) Nonparametric Regression of Covariance Structures in Longitudinal Studies. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1287
2017-11-08T18:18:32Z
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https://eprints.maths.manchester.ac.uk/1287/
Semiparametric Mean-Covariance
Regression Analysis for Longitudinal Data
Leng, Chenlei
Zhang, Weiping
Pan, Jianxin
62 Statistics
E±cient estimation of the regression coe±cients in longitudinal data anal-
ysis requires a correct speci¯cation of the covariance structure. Existing ap-
proaches usually focus on modeling the mean with speci¯cation of certain co-
variance structures, which may lead to ine±cient or biased estimators of pa-
rameters in the mean if misspeci¯cation occurs. In this paper, we propose a
data-driven approach based on semiparametric regression models for the mean
and the covariance simultaneously, motivated by the modi¯ed Cholesky de-
composition. A regression spline based approach using generalized estimating equations is developed to estimate the parameters in the mean and the covari-
ance. The resulting estimators for the regression coe±cients in both the mean
and the covariance are shown to be consistent and asymptotically normally dis-
tributed. In addition, the nonparametric functions in these two structures are
estimated at their optimal rate of convergence. Simulation studies and a real
data analysis show that the proposed approach yields highly e±cient estimators
for the parameters in the mean, and provides parsimonious estimation for the
covariance structure.
2009-07-09
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1287/1/smv0830.pdf
Leng, Chenlei and Zhang, Weiping and Pan, Jianxin (2009) Semiparametric Mean-Covariance Regression Analysis for Longitudinal Data. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1288
2017-11-08T18:18:32Z
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https://eprints.maths.manchester.ac.uk/1288/
Joint Longitudinal and Survival-cure Models
with Constrained Parameters in Tumour
Xenograft Experiments
Bao, Yanchun
Pan, Jianxin
Dai, Hongsheng
Fang, Hong-Bin
62 Statistics
In tumour xenograft experiments, treatment regimens are ad-
ministered and the tumour volume of each individual is measured repeatedly
over time. Survival data are recorded due to the death of some individuals
during the observation time period. Also, cure data are observed due to a
portion of individuals who are completely cured in the experiments. When
modelling these data, certain constraints have to be imposed on the param-
eters in the models to account for the intrinsic growth of the tumour in the
absence of treatment. Also, the likely inherent association of longitudinal
and survival-cure data has to be taken into account in order to obtain unbi-
ased estimators of parameters. In this paper, we propose such models for the
joint modelling of longitudinal and survival-cure data arising in xenograft experiments. Estimators of parameters in the joint models are obtained us-
ing a Markov chain Monte Carlo approach. Real data analysis of a xenograft
experiment is carried out and simulation studies are also conducted, show-
ing that the proposed joint modelling approach outperforms the separate
modelling methods in the sense of mean squared errors.
2009-07-09
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1288/1/tumorDec2008.pdf
Bao, Yanchun and Pan, Jianxin and Dai, Hongsheng and Fang, Hong-Bin (2009) Joint Longitudinal and Survival-cure Models with Constrained Parameters in Tumour Xenograft Experiments. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1289
2017-11-08T18:18:32Z
7374617475733D707562
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https://eprints.maths.manchester.ac.uk/1289/
Variable Selection for Joint Mean and
Covariance Models via Penalized Likelihood
Kou, Chaofeng
Pan, Jianxin
62 Statistics
In this paper, we propose a penalized maximum likelihood method for variable
selection in joint mean and covariance models for longitudinal data. Under certain
regularity conditions, we establish the consistency and asymptotic normality of the
penalized maximum likelihood estimators of parameters in the models. We further
show that the proposed estimation method can correctly identify the true models, as
if the true models would be known in advance. We also carry out real data analysis
and simulation studies to assess the small sample performance of the new procedure,
showing that the proposed variable selection method works satisfactorily
2009-07-09
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1289/1/var-selection-March09.pdf
Kou, Chaofeng and Pan, Jianxin (2009) Variable Selection for Joint Mean and Covariance Models via Penalized Likelihood. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1400
2017-11-08T18:18:32Z
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https://eprints.maths.manchester.ac.uk/1400/
An inhomogeneous stochastic rate process for evolution
from states in an information geometric neighbourhood of uniform fitness
Dodson, CTJ
62 Statistics
92 Biology and other natural sciences
This study elaborates some examples of a simple evolutionary stochastic rate process
where the population rate of change depends on the distribution of properties---so
different cohorts change at different rates. We investigate
the effect on the evolution arising from parametrized perturbations of
uniformity for the initial inhomogeneity. The information geometric
neighbourhood system yields also solutions
for a wide range of other initial inhomogeneity distributions,
including approximations to truncated Gaussians of arbitrarily small variance
and distributions with pronounced extreme values.
It is found that, under quite
considerable alterations in the shape and variance of the initial distribution of inhomogeneity
in unfitness, the decline of the mean does change markedly with the variation in starting conditions,
but the net population evolution seems surprisingly stable.
2010-01-29
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1400/1/evolmodel.pdf
Dodson, CTJ (2010) An inhomogeneous stochastic rate process for evolution from states in an information geometric neighbourhood of uniform fitness. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1665
2017-11-08T18:18:33Z
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7375626A656374733D4D5343:4D53435F3934
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https://eprints.maths.manchester.ac.uk/1665/
Stochastic production trees as products of i.i.d. componentwise exponential max-plus matrices
Hook, James
Broomhead, Dave
05 Combinatorics
15 Linear and multilinear algebra; matrix theory
37 Dynamical systems and ergodic theory
62 Statistics
92 Biology and other natural sciences
94 Information and communication, circuits
We introduce a class of stochastic production tree model, based on Petri nets, which admit a random matrix product description in the Max-plus algebra. With a kind of combinatorial change of variables we are able to simplify the form of the matrices arising from these models. For this class of \emph{Componentwise exponential} matrix we prove a new result relating the (Max-plus) spectrum of the product to the principal (classical) eigenvalue of an associated adjacency matrix by means of a sandwich inequality. This theorem highlights several important theoretical factors in the dynamics of Max-plus linear systems generally and gives us some neat insight into the different production tree models.
2011-08-18
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1665/1/Products_of_iid_componentwise_exponential_maxplus_matricies%5B1%5D.pdf
Hook, James and Broomhead, Dave (2011) Stochastic production trees as products of i.i.d. componentwise exponential max-plus matrices. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1837
2017-11-08T18:18:34Z
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https://eprints.maths.manchester.ac.uk/1837/
Covariance Structure Regularization via Entropy Loss Function
Lin, Lijing
Higham, Nicholas J.
Pan, Jianxin
62 Statistics
The need to estimate structured covariance matrices arises in a variety of applications and the problem is widely studied in statistics. We propose a new method for regularizing the covariance structure of a given covariance
matrix, in which the underlying structure is usually blurred due to random noises particularly when the dimension of the covariance matrix is high. The regularization is made
by choosing an optimal structure from an available class of covariance structures in terms of minimizing the discrepancy, defined via the entropy loss function, between the given matrix and the class. A range of potential candidate structures such as tridiagonal, compound symmetry,
AR(1), and Toeplitz are considered. Simulation studies are conducted, showing that the proposed new approach is reliable in regularization of covariance structures. The approach is also applied to real data analysis, demonstrating the usefulness of the proposed approach in practice.
2012-06-11
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1837/1/Cov-regularization.pdf
Lin, Lijing and Higham, Nicholas J. and Pan, Jianxin (2012) Covariance Structure Regularization via Entropy Loss Function. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1879
2017-11-08T18:18:35Z
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https://eprints.maths.manchester.ac.uk/1879/
A Frequency domain approach for the estimation of parameters of spatio-temporal stationary random processes
Subba Rao, Tata
Das, Sourav
Boshnakov, Georgi N.
60 Probability theory and stochastic processes
62 Statistics
In this paper we consider the estimation of the parameters of the spatio-temporal covariances of spatio-temporal stationary random processes. We define Finite Fourier Transforms of the processes at each location and based on joint distribution of these complex valued random
variables we define an approximate likelihood function and consider the maximization. Ideas are similar to Whittle likelihood function considered in time series. The sampling properties of the estimators are investigated. The method is applied to simulated data and also to pacific wind
speed data considered earlier by Cressie and Huang.
2012-10-16
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1879/1/RaoDasBoshnakov_Whittle_Likelihood.pdf
Subba Rao, Tata and Das, Sourav and Boshnakov, Georgi N. (2012) A Frequency domain approach for the estimation of parameters of spatio-temporal stationary random processes. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2020
2017-11-08T18:18:35Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2020/
Covariance Structure Regularization via Entropy Loss Function
Lin, Lijing
Higham, Nicholas J.
Pan, Jianxin
62 Statistics
The need to estimate structured covariance matrices arises in a variety of applications and the problem is widely studied in statistics. We propose a new method for regularizing the covariance structure of a given covariance
matrix, in which the underlying structure is usually blurred due to random noises particularly when the dimension of the covariance matrix is high. The regularization is made
by choosing an optimal structure from an available class of covariance structures in terms of minimizing the discrepancy, defined via the entropy loss function, between the given matrix and the class. A range of potential candidate structures such as tridiagonal, compound symmetry,
AR(1), and Toeplitz are considered. Simulation studies are conducted, showing that the proposed new approach is reliable in regularization of covariance structures. The approach is also applied to real data analysis, demonstrating the usefulness of the proposed approach in practice.
2012-06-11
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2020/1/paper.pdf
Lin, Lijing and Higham, Nicholas J. and Pan, Jianxin (2012) Covariance Structure Regularization via Entropy Loss Function. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2024
2017-11-08T18:18:35Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
7375626A656374733D4D5343:4D53435F3635
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2024/
Covariance Structure Regularization via Entropy Loss Function
Lin, Lijing
Higham, Nicholas J.
Pan, Jianxin
62 Statistics
65 Numerical analysis
The need to estimate structured covariance matrices arises in a variety of applications and the problem is widely studied in statistics. A new method is proposed for regularizing the covariance structure of a given
covariance matrix whose underlying structure has been blurred by random noise, particularly when the dimension of the covariance matrix is high. The regularization is made by choosing an optimal structure from an available class of covariance structures in terms of minimizing the discrepancy, defined via the entropy loss function, between the given matrix and the class. A range of potential candidate structures comprising tridiagonal Toeplitz, compound symmetry, AR(1), and banded Toeplitz is considered.
It is shown that for the first three structures local or global minimizers of the discrepancy can be computed by one-dimensional optimization, while for the fourth structure Newton's method enables efficient computation of the global minimizer. Simulation studies are conducted, showing that the proposed new approach provides a reliable way to regularize covariance structures. The approach is also applied to real data analysis, demonstrating the usefulness of the proposed approach in practice.
2013-10-08
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2024/1/paper_final.pdf
Lin, Lijing and Higham, Nicholas J. and Pan, Jianxin (2013) Covariance Structure Regularization via Entropy Loss Function. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2101
2017-10-20T14:13:12Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
7375626A656374733D4D5343:4D53435F3635
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2101/
Covariance Structure Regularization via Entropy Loss Function
Lin, Lijing
Higham, Nicholas J.
Pan, Jianxin
62 Statistics
65 Numerical analysis
The need to estimate structured covariance matrices arises in a variety of applications and the problem is widely studied in statistics. A new method is proposed for regularizing the covariance structure of a given
covariance matrix whose underlying structure has been blurred by random noise, particularly when the dimension of the covariance matrix is high. The regularization is made by choosing an optimal structure from an available class of covariance structures in terms of minimizing the discrepancy, defined via the entropy loss function, between the given matrix and the class. A range of potential candidate structures comprising tridiagonal Toeplitz, compound symmetry, AR(1), and banded Toeplitz is considered.
It is shown that for the first three structures local or global minimizers of the discrepancy can be computed by one-dimensional optimization, while for the fourth structure Newton's method enables efficient computation of the global minimizer. Simulation studies are conducted, showing that the proposed new approach provides a reliable way to regularize covariance structures. The approach is also applied to real data analysis, demonstrating the usefulness of the proposed approach in practice.
2014-04
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2101/1/covariance-regularization-R2_elsarticle.pdf
Lin, Lijing and Higham, Nicholas J. and Pan, Jianxin (2014) Covariance Structure Regularization via Entropy Loss Function. Computational Statistics & Data Analysis, 72. pp. 315-327. ISSN 0167-9473
http://www.sciencedirect.com/science/article/pii/S0167947313003575#
10.1016/j.csda.2013.10.004
10.1016/j.csda.2013.10.004
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2124
2017-10-20T14:13:12Z
7374617475733D7375626D6974746564
7375626A656374733D4D5343:4D53435F3630
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2124/
Tail behavior of the generalized Maxwell distribution
Huang, Jianwen
Chen, Shouquan
Tuo, Zhongyou
60 Probability theory and stochastic processes
62 Statistics
In this paper, we investigate the tail properties of the generalized Maxwell distribution and gain an asymptotic
behavior of Mills-type ratio. Meanwhile, We show two applications. The first application thinks about the asymptotic property of the ratio of density functions and the ratio of the tails of the generalized Maxwell and classical Maxwell distributions. Another application obtains the asymptotic distribution of the partial maximum of an independent and identically distributed sequence from
the distribution.
2014-01-01
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2124/1/Tail_behavior_of_generalized_Maxwell_distribution.pdf
Huang, Jianwen and Chen, Shouquan and Tuo, Zhongyou (2014) Tail behavior of the generalized Maxwell distribution. Communications in Statistics-Theory and Methods. ISSN 0361-0926 (Submitted)
http://www.tandfonline.com/toc/lsta20/current#.U0uOKbLdhj0
LSTA-2014-0001
LSTA-2014-0001
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2176
2017-11-08T18:18:36Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3630
7375626A656374733D4D5343:4D53435F3632
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2176/
Convergence rate of extremes of generalized Maxwell distribution
Huang, Jianwen
Chen, Shouquan
60 Probability theory and stochastic processes
62 Statistics
Let $\{X_n, n\geq1\}$ be a sequence of independent and identically distributed random variables with common
distribution $F$ following the generalized Maxwell distribution. In this paper, we obtain the exact uniform convergence rate of the distribution of the maximum to its extreme value distribution.
2014-09-16
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2176/1/Convergence_rate_of_extremes_of_generalized_Maxwell_distribution.pdf
Huang, Jianwen and Chen, Shouquan (2014) Convergence rate of extremes of generalized Maxwell distribution. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2187
2017-11-08T18:18:36Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
7375626A656374733D4D5343:4D53435F3635
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2187/
Statistical cluster analysis and visualisation for alarm management configuration
Butters, T D
Güttel, S
Shapiro, J L
Sharpe, T J
62 Statistics
65 Numerical analysis
The effective performance of an alarm system is a key aspect of asset management for any industrial installation. However, it is not uncommon for alarm systems to be poorly configured, leading to large amounts of alarm noise and a potentially dangerous load on the operators. Here we present a novel method for the identification of redundant or bad actors in alarm systems through the application of statistical cluster analysis. This allows the system to be optimised to reduce the load on the operators through existing systems change management processes.
2014-10-12
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2187/1/paper.pdf
Butters, T D and Güttel, S and Shapiro, J L and Sharpe, T J (2014) Statistical cluster analysis and visualisation for alarm management configuration. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2210
2017-10-20T14:13:16Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3436
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2210/
Bayesian inverse problems for functions and applications to fluid mechanics
Cotter, Simon
Dashti, Massoumeh
Robinson, James
Stuart, Andrew
46 Functional analysis
62 Statistics
In this paper we establish a mathematical framework for a range of inverse problems for functions, given a finite set of noisy observations. The problems are hence underdetermined and are often ill-posed. We study these problems from the viewpoint of Bayesian statistics, with the resulting posterior probability measure being defined on a space of functions. We develop an abstract framework for such problems which facilitates application of an infinite-dimensional version of Bayes theorem, leads to a well-posedness result for the posterior measure (continuity in a suitable probability metric with respect to changes in data), and also leads to a theory for the existence of maximizing the posterior probability (MAP) estimators for such Bayesian inverse problems on function space. A central idea underlying these results is that continuity properties and bounds on the forward model guide the choice of the prior measure for the inverse problem , leading to the desired results on well-posedness and MAP estimators; the PDE analysis and probability theory required are thus clearly dileneated, allowing a straightforward derivation of results. We show that the abstract theory applies to some concrete applications of interest by studying problems arising from data assimilation in fluid mechanics. The objective is to make inference about the underlying velocity field, on the basis of either Eulerian or Lagrangian observations. We study problems without model error, in which case the inference is on the initial condition, and problems with model error in which case the inference is on the initial condition and on the driving noise process or, equivalently, on the entire time-dependent velocity field. In order to undertake a relatively uncluttered mathematical analysis we consider the two-dimensional Navier???Stokes equation on a torus. The case of Eulerian observations???direct observations of the velocity field itself???is then a model for weather forecasting. The case of Lagrangian observations???observations of passive tracers advected by the flow???is then a model for data arising in oceanography. The methodology which we describe herein may be applied to many other inverse problems in which it is of interest to find, given observations, an infinite-dimensional object, such as the initial condition for a PDE. A similar approach might be adopted, for example, to determine an appropriate mathematical setting for the inverse problem of determining an unknown tensor arising in a constitutive law for a PDE, given observations of the solution. The paper is structured so that the abstract theory can be read independently of the particular problems in fluid mechanics which are subsequently studied by application of the theory.
2009
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2210/1/20140149.full.pdf
Cotter, Simon and Dashti, Massoumeh and Robinson, James and Stuart, Andrew (2009) Bayesian inverse problems for functions and applications to fluid mechanics. Inverse Problems, 25 (11).
10.1088/0266-5611/25/11/115008
10.1088/0266-5611/25/11/115008
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2213
2017-10-20T14:13:16Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
7375626A656374733D4D5343:4D53435F3736
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2213/
Variational data assimilation using targetted random walks
Cotter, Simon
Dashti, Massoumeh
Stuart, Andrew
62 Statistics
76 Fluid mechanics
The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis. In either of these scenarios, it can be important to assess uncertainties in the assimilated state. Ideally, it is desirable to have complete information concerning the Bayesian posterior distribution for unknown state given data. We show that complete computational probing of this posterior distribution is now within the reach in the offline situation. We introduce a Markov chain�Monte Carlo (MCMC) method which enables us to directly sample from the Bayesian posterior distribution on the unknown functions of interest given observations. Since we are aware that these methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk-type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however, more sophisticated MCMC methods are available which exploit derivative information. For simplicity of exposition, we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number flow in a two-dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces.
2012
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2213/1/2510_ftp.pdf
Cotter, Simon and Dashti, Massoumeh and Stuart, Andrew (2012) Variational data assimilation using targetted random walks. International Journal for Numerical Methods in Fluids, 68 (4). pp. 403-421.
10.1002/fld.2510
10.1002/fld.2510
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2214
2017-10-20T14:13:16Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
7375626A656374733D4D5343:4D53435F3736
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2214/
Bayesian data assimilation in shape registration
Cotter, Colin
Cotter, Simon
Vialard, Francois-Xavier
62 Statistics
76 Fluid mechanics
In this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions for the conjugate momentum onto topologically equivalent shapes. Here, we aim to recover the well-defined posterior distribution on the initial momentum which gives rise to observed points on the target curve; this is achieved by explicitly including a reparameterization in the formulation. Appropriate priors are chosen for the functions which together determine this field and the positions of the observation points, the initial momentum p0 and the reparameterization vector field ν, informed by regularity results about the forward model. Having done this, we illustrate how maximum likelihood estimators can be used to find regions of high posterior density, but also how we can apply recently developed Markov chain Monte Carlo methods on function spaces to characterize the whole of the posterior density. These illustrative examples also include scenarios where the posterior distribution is multimodal and irregular, leading us to the conclusion that knowledge of a state of global maximal posterior density does not always give us the whole picture, and full posterior sampling can give better quantification of likely states and the overall uncertainty inherent in the problem.
2013
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2214/1/0266-5611_29_4_045011.pdf
Cotter, Colin and Cotter, Simon and Vialard, Francois-Xavier (2013) Bayesian data assimilation in shape registration. Inverse Problems, 29 (4).
10.1088/0266-5611/29/4/045011
10.1088/0266-5611/29/4/045011
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2215
2017-10-20T14:13:16Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2215/
MCMC Methods for Functions: Modifying
Old Algorithms to Make Them Faster
Cotter, Simon
Roberts, Gareth
Stuart, Andrew
White, David
62 Statistics
Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become arbitrarily slow under the mesh refinement dictated by nonparametric description of the un- known function. We describe an approach to modifying a whole range of MCMC methods, applicable whenever the target measure has density with respect to a Gaussian process or Gaussian random field reference measure, which ensures that their speed of convergence is robust under mesh refinement.
Gaussian processes or random fields are fields whose marginal distri- butions, when evaluated at any finite set of N points, are RN-valued Gaussians. The algorithmic approach that we describe is applicable not only when the desired probability measure has density with respect to a Gaussian process or Gaussian random field reference measure, but also to some useful non-Gaussian reference measures constructed through random truncation. In the applications of interest the data is often sparse and the prior specification is an essential part of the over- all modelling strategy. These Gaussian-based reference measures are a very flexible modelling tool, finding wide-ranging application. Examples are shown in density estimation, data assimilation in fluid mechanics, subsurface geophysics and image registration.
The key design principle is to formulate the MCMC method so that it is, in principle, applicable for functions; this may be achieved by use of proposals based on carefully chosen time-discretizations of stochas- tic dynamical systems which exactly preserve the Gaussian reference measure. Taking this approach leads to many new algorithms which can be implemented via minor modification of existing algorithms, yet which show enormous speed-up on a wide range of applied problems.
2013
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2215/1/1202.0709v3.pdf
Cotter, Simon and Roberts, Gareth and Stuart, Andrew and White, David (2013) MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster. Statistical Science, 28 (3). pp. 424-446.
10.1214/13-STS421
10.1214/13-STS421
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2371
2017-11-08T18:18:37Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
7375626A656374733D4D5343:4D53435F3635
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2371/
Parallel Adaptive Importance Sampling
Cotter, Colin
Cotter, Simon
Russell, Paul
62 Statistics
65 Numerical analysis
Markov chain Monte Carlo methods are a powerful and commonly used family of numerical methods for sampling from complex probability distributions. As applications of these methods increase in size and complexity, the need for efficient methods which can exploit the parallel architectures which are prevalent in high performance computing increases. In this paper, we aim to develop a framework for scalable parallel MCMC algorithms. At each iteration, an importance sampling proposal distribution is formed using the current states of all of the chains within an ensemble. Once weighted samples have been produced from this, a state-of-the-art resampling method is then used to create an evenly weighted sample ready for the next iteration. We demonstrate that this parallel adaptive importance sampling (PAIS) method outperforms naive parallelisation of serial MCMC methods using the same number of processors, for low dimensional problems, and in fact shows better than linear improvements in convergence rates with respect to the number of processors used.
2015-09-03
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2371/1/PAIS.pdf
Cotter, Colin and Cotter, Simon and Russell, Paul (2015) Parallel Adaptive Importance Sampling. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2381
2017-10-20T14:13:22Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3533
7375626A656374733D4D5343:4D53435F3632
7375626A656374733D4D5343:4D53435F3934
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2381/
A model for Gaussian perturbations of graphene
Dodson, CTJ
53 Differential geometry
62 Statistics
94 Information and communication, circuits
Graphene consists nominally of a regular planar hexagonal carbon lattice monolayer. However,
its structure experiences perturbations in the presence of external influences,
whether from substrate properties, thermal or electromagnetic fields, or ambient fluid movement.
Here we give an information geometric
model to represent the state space of perturbations as a Riemannian pseudosphere with
scalar curvature close to -1/2. This would allow the
representation of a trajectory of states under a given ambient or process change,
so opening the possibility for geometrically formulated
dynamical models to link structural perturbations to
the physics.
2015-09-15
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2381/1/GrapheneModel.pdf
Dodson, CTJ (2015) A model for Gaussian perturbations of graphene. Journal of Statistical Physics, Online. pp. 1-9. ISSN 1572-9613
10.1007/s10955-015-1362-2
10.1007/s10955-015-1362-2
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2382
2017-11-08T18:18:38Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3632
7375626A656374733D4D5343:4D53435F3635
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2382/
Automatic real-time fault detection for industrial assets using metasensors
Butters, T D
Güttel, S
Shapiro, J L
Sharpe, T J
62 Statistics
65 Numerical analysis
Large-scale industrial plants require physical sensors to continuously measure quantities such as temperatures or pressures. A large number of sensors is required to accurately describe the operating state of the plant, which unfortunately makes it very difficult for them to be effectively monitored by human operators. In this work we present a method to construct so-called metasensors, virtual sensors that compress the information from several sensors in an optimal manner. These metasensors are used as inputs to a novel anomaly detection system that automatically alerts operators to abnormal operation behaviour.
2015-09-15
MIMS Preprint
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2382/1/paper.pdf
Butters, T D and Güttel, S and Shapiro, J L and Sharpe, T J (2015) Automatic real-time fault detection for industrial assets using metasensors. [MIMS Preprint]
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2406
2017-10-20T14:13:23Z
7374617475733D756E707562
7375626A656374733D4D5343:4D53435F3439
7375626A656374733D4D5343:4D53435F3630
7375626A656374733D4D5343:4D53435F3632
74797065733D746865736973
https://eprints.maths.manchester.ac.uk/2406/
Modelling and controlling risk in energy systems
Gonzalez, J
49 Calculus of variations and optimal control; optimization
60 Probability theory and stochastic processes
62 Statistics
The Autonomic Power System (APS) grand challenge was a multi-disciplinary EPSRC-funded research project that examined novel techniques that would enable the transition between today's and 2050's highly uncertain and complex energy network. Being part of the APS, this thesis reports on the sub-project `RR2: Avoiding High-Impact Low Probability events'. The goal of RR2 is to develop new algorithms for controlling risk exposure to high-impact low probability (Hi-Lo) events through the provision of appropriate risk-sensitive control strategies. Additionally, RR2 is concerned with new techniques for identifying and modelling risk in future energy networks, in particular, the risk of Hi-Lo events.
In this context, this thesis investigates two distinct problems arising from energy risk management. On the one hand, we examine the problem of finding managerial strategies for exercising the operational flexibility of energy assets. We look at this problem from a risk perspective taking into account non-linear risk preferences of energy asset managers. Our main contribution is the development of a risk-sensitive approach to the class of optimal switching problems. By recasting the problem as an iterative optimal stopping problem, we are able to characterise the optimal risk-sensitive switching strategies. As byproduct, we obtain a multiplicative dynamic programming equation for the value function, upon which we propose a numerical algorithm based on least squares Monte Carlo regression.
On the other hand, we develop tools to identify and model the risk factors faced by energy asset managers. For this, we consider a class of models consisting of superposition of Gaussian and non-Gaussian Ornstein-Uhlenbeck processes. Our main contribution is the development of a Bayesian methodology based on Markov chain Monte Carlo (MCMC) algorithms to make inference into this class of models. On extensive simulations, we demonstrate the robustness and efficiency of the algorithms to different data features. Furthermore, we construct a diagnostic tool based on Bayesian p-values to check goodness-of-fit of the models on a Bayesian framework. We apply this tool to MCMC results from fitting historical electricity and gas spot price datasets corresponding to the UK and German energy markets. Our analysis demonstrates that the MCMC-estimated models are able to capture not only long- and short-lived positive price spikes, but also short-lived negative price spikes which are typical of UK gas prices and German electricity prices.
Combining together the solutions to the two problems above, we strive to capture the interplay between risk, uncertainty, flexibility and performance in various applications to energy systems. In these applications, which include power stations, energy storage and district energy systems, we consistently show that our risk management methodology offers a tradeoff between maximising average performance and minimising risk, while accounting for the jump dynamics of energy prices. Moreover, the tradeoff is achieved in such way that the benefits in terms of risk reduction outweigh the loss in average performance.
2015-06
Thesis
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2406/1/PhDthesis_Jhonny_Gonzalez.pdf
Gonzalez, J (2015) Modelling and controlling risk in energy systems. Doctoral thesis, The University of Manchester.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2515
2017-10-20T14:13:28Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3533
7375626A656374733D4D5343:4D53435F3630
7375626A656374733D4D5343:4D53435F3632
7375626A656374733D4D5343:4D53435F3638
7375626A656374733D4D5343:4D53435F3934
74797065733D626F6F6B
https://eprints.maths.manchester.ac.uk/2515/
Computational Information Geometry For Image and Signal Processing
53 Differential geometry
60 Probability theory and stochastic processes
62 Statistics
68 Computer science
94 Information and communication, circuits
This book focuses on the application and development of information geometric methods in the analysis, classification and retrieval of images and signals. It provides introductory chapters to help those new to information geometry and applies the theory to several applications. This area has developed rapidly over recent years, propelled by the major theoretical developments in information geometry, efficient data and image acquisition and the desire to process and interpret large databases of digital information. The book addresses both the transfer of methodology to practitioners involved in database analysis and in its efficient computational implementation.
Springer
Nielsen, Frank
Critchley, Frank
Dodson, Christopher TJ
2017-01
Book
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2515/1/160209KCIGSIP-Preface.pdf
Nielsen, Frank and Critchley, Frank and Dodson, Christopher TJ, eds. (2017) Computational Information Geometry For Image and Signal Processing. Signals and Communication Technology . Springer, Germany. ISBN 978-3-319-47058-0
http://www.springer.com/gb/book/9783319470566
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2518
2017-10-20T14:13:28Z
7374617475733D707562
7375626A656374733D4D5343:4D53435F3533
7375626A656374733D4D5343:4D53435F3632
74797065733D626F6F6B5F73656374696F6E
https://eprints.maths.manchester.ac.uk/2518/
Dimensionality Reduction for Information Geometric Characterization of Surface Topographies
Dodson, CTJ
Mettanen, M
Sampson, WW
53 Differential geometry
62 Statistics
Stochastic textures with features spanning many length scales arise in a range
of contexts in physical and natural sciences, from nanostructures like synthetic bone
to ocean wave height distributions and
cosmic phenomena like inter-galactic cluster void distributions.
Here we used a data set of 35 surface topographies, each of 2400x2400 pixels
with spatial resolution between 4~\mum\ and 7~\mum\ per pixel, and fitted trivariate
Gaussian distributions to represent their spatial structures.
For these we computed pairwise information metric distances using the Fisher-Rao metric.
Then dimensionality reduction was used to reveal the groupings among subsets of samples
in an easily comprehended graphic in 3-space. The samples here came from the
papermaking industry but such a reduction of large frequently noisy spatial data
sets is useful in a range of materials and contexts at all scales.
Springer
2017
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2518/1/Dodson-DimensionalityReductionForInformationGeometricCharacterizationOfSurfaceTopographies.pdf
Dodson, CTJ and Mettanen, M and Sampson, WW (2017) Dimensionality Reduction for Information Geometric Characterization of Surface Topographies. In: Computational Information Geometry: For Image And Signal Processing. Signals and Communication Technology . Springer, Switzerland, pp. 133-147. ISBN 978-3-319-47058-0
http://www.springer.com/gp/book/9783319470566#aboutBook
http://www.springer.com/gp/book/9783319470566#aboutBook
http://www.springer.com/gp/book/9783319470566#aboutBook
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2523
2017-10-20T14:13:28Z
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https://eprints.maths.manchester.ac.uk/2523/
On some information geometric approaches to cyber security
Dodson, CTJ
53 Differential geometry
62 Statistics
Various contexts of relevance to cyber security involve the analysis of data
that has a statistical character and in some cases the extraction of particular
features from datasets of fitted distributions or empirical frequency distributions.
Such statistics, for example,
may be collected in the automated monitoring of IP-related data
during accessing or attempted accessing of web-based resources, or may be
triggered through an alert for suspected cyber attacks.
Information geometry provides a Riemannian geometric framework in which to
study smoothly parametrized families of probability density functions, thereby
allowing the use of geometric tools to study statistical features of processes
and possibly the representation of features that are associated with attacks.
In particular, we can obtain mutual distances among members of the family
from a collection of datasets, allowing for example measures of departures
from Poisson random or uniformity, and discrimination between nearby distributions.
Moreover, this allows the representation of large numbers of datasets
in a way that respects any topological features in the frequency data
and reveals subgroupings in the datasets using dimensionality reduction.
Here some results are reported on statistical and information geometric studies
concerning pseudorandom sequences, encryption-decryption timing analyses,
comparisons of nearby signal distributions and departure from uniformity for
evaluating obscuring techniques.
Springer
Daras, Nicholas J
Rassias, Thermistocles M
2017-03
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2523/1/DodsonCyberSecurityFinal.pdf
Dodson, CTJ (2017) On some information geometric approaches to cyber security. In: Operations Research, Engineering, and Cyber Security. Springer Optimization and Its Applications (113). Springer, Germany. (In Press)
http://www.springer.com/gb/book/9783319514987
http://www.springer.com/gb/book/9783319514987
http://www.springer.com/gb/book/9783319514987
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2669
2018-10-21T09:02:30Z
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https://eprints.maths.manchester.ac.uk/2669/
Face recognition based on texture information and geodesic distance approximations between multivariate normal distributions
Soldera, J
Dodson, CTJ
Scharkanski, J
53 Differential geometry
62 Statistics
Geodesic distance is a natural dissimilarity measure between
probability distributions of a specific type, and can be used to
discriminate texture in image-based measurements. Furthermore, since
there is no known closed-form solution for the geodesic distance
between general multivariate normal distributions, we propose two
efficient approximations to be used as texture dissimilarity metrics
in the context of face recognition. A novel face recognition
approach based on texture discrimination in high-resolution color
face images is proposed, unlike the typical appearance-based
approach that relies on low-resolution grayscale face images. In our
face recognition approach, sparse facial features are extracted
using predefined landmark topologies, that identify discriminative
image locations on the face images. Given this landmark topology,
the dissimilarity between distinct face images are scored in terms
of the dissimilarities between their corresponding face landmarks,
and the texture in each one of these landmarks is represented by
multivariate normal distributions, expressing the color distribution
in the vicinity of each landmark location. The classification of new
face image samples occurs by determining the face image sample in
the training set which minimizes the dissimilarity score, using the
nearest neighbor rule. The proposed face recognition method was
compared to methods representative of the state-of-the-art, using
color or grayscale face images, and presented higher recognition
rates. Moreover, the proposed texture dissimilarity metric also is
efficient in general texture discrimination (e.g., texture
recognition of material images), as our experiments suggest.
IOP Publishing Ltd
2018-10-03
Article
PeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2669/1/Soldera_2018_Meas._Sci._Technol._29_114001.pdf
Soldera, J and Dodson, CTJ and Scharkanski, J (2018) Face recognition based on texture information and geodesic distance approximations between multivariate normal distributions. Measurement Science and Technology, 29 (11). pp. 1-9. ISSN ISSN: 1361-6501
http://iopscience.iop.org/article/10.1088/1361-6501/aade18
10.1088/1361-6501/aade18
10.1088/1361-6501/aade18
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2827
2021-07-11T08:44:41Z
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https://eprints.maths.manchester.ac.uk/2827/
Some Information Geometric Aspects of Cyber Security by Face Recognition
Dodson, CTJ
Soldera, John
Scharcanski, J
53 Differential geometry
60 Probability theory and stochastic processes
62 Statistics
Secure user access to devices and datasets is widely enabled by fingerprint or face recognition.
Organization of the necessarily large secure digital object datasets, with objects
having content that may consist of images,
text, video or audio, involves efficient classification and feature
retrieval processing. This usually will require multidimensional methods applicable
to data that is represented through a family of probability distributions.
Then information geometry is an appropriate context
in which to provide for such analytic work, whether with maximum likelihood fitted
distributions or empirical frequency distributions. The important provision is of
a natural geometric measure structure on families of probability
distributions by representing them as Riemannian manifolds.
Then the distributions are points lying in this geometrical manifold, different features
can be identified and dissimilarities
computed, so that neighbourhoods of objects nearby a given example object can be
constructed. This can reveal clustering and projections onto smaller eigen-subspaces
which can make comparisons easier to interpret. Geodesic distances can be used as a natural
dissimilarity metric applied over data described by probability distributions. Exploring this
property, we propose a new face recognition method which scores dissimilarities between face
images by multiplying geodesic distance approximations between $3$-variate RGB Gaussians
representative of colour face images, and also obtaining joint probabilities. The experimental results show that this new method
is more successful in recognition rates than published comparative state-of-the-art methods.
MDPI
2021-07-09
Article
PeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2827/1/entropy-23-00878.pdf
Dodson, CTJ and Soldera, John and Scharcanski, J (2021) Some Information Geometric Aspects of Cyber Security by Face Recognition. Entropy, 23 (878). pp. 1-10.
https://www.mdpi.com/1099-4300/23/7/878/pdf
doi.org/10.3390/e23070878
doi.org/10.3390/e23070878
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2851
2022-03-12T09:57:19Z
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https://eprints.maths.manchester.ac.uk/2851/
An approach to protein structure using information geometry
Dodson, CTJ
60 Probability theory and stochastic processes
62 Statistics
In the light of recent structural developments in DNA structural diversity crystallographic studies and the Protein Data Bank*, this note is intended to draw attention to an interesting feature of the ordering of amino acids along protein chains. They all exhibited clustering compared to a random
distribution, so there is a stable long range ordering that is unexpected. To date
we have no clear explanation of why this should be the case.
* https://doi.org/10.1016/j.jbc.2021.100553.
2022-02-16
Article
PeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2851/1/AJBSR.MS.ID.002123.pdf
Dodson, CTJ (2022) An approach to protein structure using information geometry. American J Biomedical Sciences and Research. pp. 371-373. ISSN 2642-1747
https://biomedgrid.com/pdf/AJBSR.MS.ID.002123.pdf
DOI: 10.34297/AJBSR.2022.15.002123
DOI: 10.34297/AJBSR.2022.15.002123
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2884
2023-03-29T17:22:57Z
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https://eprints.maths.manchester.ac.uk/2884/
Modelling and classifying joint trajectories of self-reported mood and pain in a large cohort study
Das, Rajenki
Muldoon, Mark
Lunt, Mark
McBeth, John
Yimer, Belay Birlie
House, Thomas
62 Statistics
92 Biology and other natural sciences
It is well-known that mood and pain interact with each other, however individual-level variability in this relationship has been less well quantified than overall associations between low mood and pain. Here, we leverage the possibilities presented by mobile health data, in particular the “Cloudy with a Chance of Pain” study, which collected longitudinal data from the residents of the UK with chronic pain conditions. Participants used an App to record self-reported measures of factors including mood, pain and sleep quality. The richness of these data allows us to perform model-based clustering of the data as a mixture of Markov processes. Through this analysis we discover four endotypes with distinct patterns of co-evolution of mood and pain over time. The differences between endotypes are sufficiently large to play a role in clinical hypothesis generation for personalised treatments of comorbid pain and low mood.
2023-03-30
Article
PeerReviewed
text
en
cc_by_4
https://eprints.maths.manchester.ac.uk/2884/1/pdig.0000204.pdf
Das, Rajenki and Muldoon, Mark and Lunt, Mark and McBeth, John and Yimer, Belay Birlie and House, Thomas (2023) Modelling and classifying joint trajectories of self-reported mood and pain in a large cohort study. PLOS Digital Health, 2 (3). e0000204. ISSN 2767-3170 (In Press)
10.1371/journal.pdig.0000204
10.1371/journal.pdig.0000204