Some illustrations of information geometry in biology and physics

Dodson, CTJ (2011) Some illustrations of information geometry in biology and physics. In: Handbook of Research on Computational Science and Engineering: Theory and Practice. IGI-Global, Hershey, USA, pp. 1-27. ISBN 9781613501160 (In Press)

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Abstract

Many real processes have stochastic features which seem to be representable in some intuitive sense as `close to Poisson', `nearly random', `nearly uniform' or with binary variables `nearly independent'. Each of those particular reference states, defined by an equation, is unstable in the formal sense, but it is passed through or hovered about by the observed process. Information geometry gives precise meaning for nearness and neighbourhood in a state space of processes, naturally quantifying proximity of a process to a particular state via an information theoretic metric structure on smoothly parametrized families of probability density functions. We illustrate some aspects of the methodology through case studies: inhomogeneous statistical evolutionary rate processes for epidemics, amino acid spacings along protein chains, constrained disordering of crystals, distinguishing nearby signal distributions and testing pseudorandom number generators.

Item Type: Book Section
Uncontrolled Keywords: Families of probability densities, gamma distributions, information geometry, amino acids, constrained disordering, evolution, epidemic, inhomogeneous rate process, entropy, analytic and numerical computation.
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry
MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Prof CTJ Dodson
Date Deposited: 04 Aug 2011
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1662

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