Dodson, CTJ (2005) Topics in Information Geometry. In: Workshop on Recent Results in Information Geometry, 13-19 Dec 2005, Santiago de Compostela, Spain. (Unpublished)
![[thumbnail of InfoGeom.pdf]](https://eprints.maths.manchester.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
InfoGeom.pdf Download (1MB) |
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: | https://eprints.maths.manchester.ac.uk/id/eprint/131 |
Actions (login required)
 |
View Item |