Topics in Information Geometry

Dodson, CTJ (2005) Topics in Information Geometry. In: Workshop on Recent Results in Information Geometry, 13-19 Dec 2005, Santiago de Compostela, Spain. (Unpublished)

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Abstract

We introduce first some of the background ideas on information theory and its role in studying analytic models for stochastic processes and the geometrization of families of measure functions. This is then used to present the geometry of important examples of the Riemannian manifolds that arise. Next, we obtain the proof of two theorems that characterise the metric neighbourhoods of the two distinguished fundamental states: randomness and independence. These methods have had applications in modelling cryptographic attacks, cosmological void distributions, porous media, clustering of: galaxies, communications, and amino acids along protein chains in genomes.

Item Type: Conference or Workshop Item (Lecture)
Additional Information: Mathematica Notebooks available from the author for computational examples.
Uncontrolled Keywords: Information theory, information geometry, Fisher metric, connection, curvature, universal connection, exponential family, alpha connection, McKay manifold, Freund manifold, gamma manifold, random, independent, clustering, applications,cryptographic attacks, cosmological void distributions, porous media,galaxies, communications, amino acids
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: 17 Dec 2005
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/131

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