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

Cohen, Joel E.; Kemperman, J. H. B.; Zbăganu, Gheorghe

Hardcover

ISBN 10: 0817640827 ISBN 13: 9780817640828

Verlag: Birkhäuser, 1998

Inhaltsangabe

The focus of this monograph is on generalizing the notion of variation in a set of numbers to variation in a set of probability distributions.  The authors collect some known ways of comparing stochastic matrices in the context of information theory, statistics, economics, and population sciences.  They then generalize these comparisons, introduce new comparisons, and establish the relations of implication or equivalence among sixteen of these comparisons.  Some of the possible implications among these comparisons remain open questions.  The results in this book establish a new field of investigation for both mathematicians and scientific users interested in the variations among multiple probability distributions.

The work is divided into two parts.  The first deals with finite stochastic matrices, which may be interpreted as collections of discrete probability distributions.  The first part is presented in a fairly elementary mathematical setting. The introduction provides sketches of applications of concepts and methods to discrete memory-less channels in information theory, to the design and comparison of experiments in statistics, to the measurement of inequality in economics, and to various analytical problems in population genetics, ecology, and demography.  Part two is more general and entails more difficult analysis involving Markov kernels.  Here, many results of the first part are placed in a more general setting, as required in more sophisticated applications.

A great strength of this text is the resulting connections among ideas from diverse fields: mathematics, statistics, economics, and population biology.  In providing this array of new tools and concepts, the work will appeal to the practitioner.  At the same time, it will serve as an excellent resource for self-study of for a graduate seminar course, as well as a stimulus to further research.

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Über die Autorin bzw. den Autor

Kenneth G. Manton, Ph.D. is Research Professor, Research Director, and Director of the Center for Demographic Studies at Duke University, and Medical Research Professor at Duke University Medical Center's Department of Community and Family Medicine. Dr. Manton is also a Senior Fellow of the Duke University Medical Center's Center for the Study of Aging and Human Development. His research interests include mathematical models of human aging, mortality, and chronic disease. He was the 1990 recipient of the Mindel C. Sheps Award in Mathematical Demography presented by the Population Association of America; and in 1991 he received the Allied-Signal Inc. Achievement Award in Aging administered by the Johns Hopkins Center on Aging. Joel E. Cohen, Ph.D., Dr. P.H., is Professor of Population, and Head of the Laboratory of Populations, Rockefeller University. He also is Professor of Populations at Columbia University. His research interests include the demography, ecology, epidemiology, and social organization of human and non-human populations, and related mathematical concepts. In 1981, he was elected Fellow of the MacArthur and Guggeneheim Foundations. He was the 1992 recipient of the Mindel C. Sheps Award in Mathematical Demography presented by the Population Association of America; and in 1994, he received the Distinguished Statistical Ecologist Award at the Sixth International Congress of Ecology.

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The focus of this monograph is on generalizing the notion of variation in a set of numbers to variation in a set of probability distributions.  The authors collect some known ways of comparing stochastic matrices in the context of information theory, statistics, economics, and population sciences.  They then generalize these comparisons, introduce new comparisons, and establish the relations of implication or equivalence among sixteen of these comparisons.  Some of the possible implications among these comparisons remain open questions.  The results in this book establish a new field of investigation for both mathematicians and scientific users interested in the variations among multiple probability distributions.

The work is divided into two parts.  The first deals with finite stochastic matrices, which may be interpreted as collections of discrete probability distributions.  The first part is presented in a fairly elementary mathematical setting. The introduction provides sketches of applications of concepts and methods to discrete memory-less channels in information theory, to the design and comparison of experiments in statistics, to the measurement of inequality in economics, and to various analytical problems in population genetics, ecology, and demography.  Part two is more general and entails more difficult analysis involving Markov kernels.  Here, many results of the first part are placed in a more general setting, as required in more sophisticated applications.

A great strength of this text is the resulting connections among ideas from diverse fields: mathematics, statistics, economics, and population biology.  In providing this array of new tools and concepts, the work will appeal to the practitioner.  At the same time, it will serve as an excellent resource for self-study of for a graduate seminar course, as well as a stimulus to further research.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 1998
• Sprache: Englisch
• ISBN 10: 0817640827
• ISBN 13: 9780817640828
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 166
• Kontakt zum Hersteller: preigu GmbH & Co. KG; mail@preigu.de; ; Lengericher Landstr. 19; Osnabrück; Niedersachsen; 49078; Deutschland