Comparisons of Stochastic Matrices with Applications in Information Theory, Statistics, Economics and Population / Edition 1

Comparisons of Stochastic Matrices with Applications in Information Theory, Statistics, Economics and Population / Edition 1

by JOEL Cohen, J.H.B. Kempermann, G. Zbaganu
     
 

ISBN-10: 0817640827

ISBN-13: 9780817640828

Pub. Date: 09/29/1998

Publisher: Birkhauser Verlag

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

Overview

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.

Product Details

ISBN-13:
9780817640828
Publisher:
Birkhauser Verlag
Publication date:
09/29/1998
Edition description:
1998
Pages:
158
Product dimensions:
0.44(w) x 6.14(h) x 9.21(d)

Table of Contents

Preface
Pt. I: Comparing Partial Orderings Among Stochastic Matrices
Joel E. Cohen, J. H. B. Kemperman, Gh. Zbaganu
1: Introduction
2: Notation and definitions
3: Generalizations of classical channel comparisons
4: Degradation is the same as increasing density
5: Shannon's inclusion implies smaller capacity
6: A simple case: matrices A and B have only two columns
7: Open problems
Pt. II: Divergence and Contraction Coefficients
Gh. Zbaganu
1: Introduction, definitions, and notation
2: A generalization of an inequality of Dobrushin
3: The divergence
4: Divergence between images of measures via Markov kernels. Contraction coefficients
5: A particular case: At most countable spaces
6: Behavior of (actual symbol not reproducible) for a fixed Markov kernel T
7: Applications of global divergence to comparison of experiments
8: History of the problem
References
Index of principal notations
Index

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