Comparisons of Stochastic Matrices with Applications in Information Theory, Statistics, Economics and Population

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September 1998



This book generalizes the notion of variation in a set of numbers to variation in a set of probability distributions. It deals with finite stochastic matrices and is presented in an elementary mathematical setting. The introduction, for example, examines applications of concepts and methods in information theory, statistics, economics, and population sciences (population genetics, ecology and demography). Gradually, the exposition becomes more technical, dealing with Markov kernels as generalizations of stochastic matrices.Stochastic matrices are compared in the context of memoryless channels in information theory; the comparisons are then generalized, and in turn, lead to new implications and results that will add to an array of new concepts and tools for the practitioner.The overall scope of this work shows important connections among ideas from diverse fields including mathematics, economics, and biology. Its clarity of presentation makes this a resource or a good for self-study or for graduate course.


Part 1 Partial orderings among stochastic matrices, Joel E. Cohen et al: introduction; notation and definitions; generalizations of classical channel comparisons; degradation is the same as increasing density; Shannon's inclusion implies smaller capacity; a simple case - matrices A and B haver only two columns; open problems. Part 2 Divergence and contraction coefficients, Gh. Zbaganu: introduction, definitions and notations; a generalization of an inequality of Dobrushin; the divergence; divergence between images of measures via Markov kernels -contraction coefficients; a particular case - at most countable spaces; behaviour of phi-eta phi(tau) for a fixed Markov kernel tau; applications of global divergences to comparison of experiments; history of the problem.


"This book gives a mathematical treatment of a variety of methods for quantifying divergence or similarity between sets of proability distributions on a common space. Classical metrics, such as total variation and Kullback--Liebler divergence, are generalized. Such problems arise in statistics, economics and information theory. The book gives Brief but useful treatments of these and other applications with abundant references... well written with pointers to history and other methods of proof."
--Journal of the American Statistical Assoc.
"The book is compact and is dense with information. There is considerable motivation in the introduction... Contain[s] much material for the specialist."
--Zentralblatt Math
EAN: 9780817640828
ISBN: 0817640827
Untertitel: 1998. Auflage. Book. Sprache: Englisch.
Verlag: Birkhäuser
Erscheinungsdatum: September 1998
Seitenanzahl: 168 Seiten
Format: gebunden
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