Information Geometry: Near Randomness and Near Independence

ISBN-13: 9783540693918 / Angielski / Miękka / 2008 / 272 str.

Khadiga Arwini

Opis

The main motivation for this book lies in the breadth of applications in which a statistical model is used to represent small departures from, for example, a Poisson process. Our approach uses information geometry to provide a c- mon context but we need only rather elementary material from di?erential geometry, information theory and mathematical statistics. Introductory s- tions serve together to help those interested from the applications side in making use of our methods and results. We have available Mathematica no- books to perform many of the computations for those who wish to pursue their own calculations or developments. Some 44 years ago, the second author ?rst encountered, at about the same time, di?erential geometry via relativity from Weyl s book 209] during - dergraduate studies and information theory from Tribus 200, 201] via spatial statistical processes while working on research projects at Wiggins Teape - searchandDevelopmentLtd cf. theForewordin 196]and 170,47,58]. H- ing started work there as a student laboratory assistant in 1959, this research environment engendered a recognition of the importance of international c- laboration, and a lifelong research interest in randomness and near-Poisson statistical geometric processes, persisting at various rates through a career mainly involved with global di?erential geometry. From correspondence in the 1960s with Gabriel Kron 4, 124, 125] on his Diakoptics, and with Kazuo Kondo who in?uenced the post-war Japanese schools of di?erential geometry and supervised Shun-ichi Amari s doctorate 6], it was clear that both had a much wider remit than traditionally pursued elsewhere."

Spis treści

Mathematical Statistics and Information Theory.- to Riemannian Geometry.- Information Geometry.- Information Geometry of Bivariate Families.- Neighbourhoods of Poisson Randomness, Independence, and Uniformity.- Cosmological Voids and Galactic Clustering.- Amino Acid Clustering.- Cryptographic Attacks and Signal Clustering.- Stochastic Fibre Networks.- Stochastic Porous Media and Hydrology.- Quantum Chaology.

Blurb

This volume will be useful to practising scientists and students working in the application of statistical models to real materials or to processes with perturbations of a Poisson process, a uniform process, or a state of independence for a bivariate process. We use information geometry to provide a common differential geometric framework for a wide range of illustrative applications including amino acid sequence spacings in protein chains, cryptology studies, clustering of communications and galaxies, cosmological voids, coupled spatial statistics in stochastic fibre networks and stochastic porous media, quantum chaology. Introduction sections are provided to mathematical statistics, differential geometry and the information geometry of spaces of probability density functions.