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.
Author(s): Khadiga A. Arwini, Christopher T. J. Dodson (auth.)
Series: Lecture Notes in Mathematics 1953
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2008
Language: English
Pages: 260
Tags: Differential Geometry; Probability Theory and Stochastic Processes; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences; Continuum Mechanics and Mechanics of Materials; Genetics and Population Dynamics
Front Matter....Pages I-X
Mathematical Statistics and Information Theory....Pages 1-18
Introduction to Riemannian Geometry....Pages 19-30
Information Geometry....Pages 31-54
Information Geometry of Bivariate Families....Pages 55-107
Neighbourhoods of Poisson Randomness, Independence, and Uniformity....Pages 109-117
Cosmological Voids and Galactic Clustering....Pages 119-137
Amino Acid Clustering....Pages 139-151
Cryptographic Attacks and Signal Clustering....Pages 153-159
Stochastic Fibre Networks....Pages 161-194
Stochastic Porous Media and Hydrology....Pages 195-222
Quantum Chaology....Pages 223-233
Back Matter....Pages 235-253
