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Books > Science & Mathematics > Mathematics > Applied mathematics > Stochastics
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Comparisons of Stochastic Matrices with Applications in Information Theory, Statistics, Economics and Population Sciences (Hardcover, 1998 ed.)
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Comparisons of Stochastic Matrices with Applications in Information Theory, Statistics, Economics and Population Sciences (Hardcover, 1998 ed.)
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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.
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