The focus of this work 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. 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 or for a graduate seminar course, as well as a stimulus to further research.
Publisher: Birkhauser Boston Inc
Number of pages: 158
Weight: 920 g
Dimensions: 235 x 155 x 11 mm
Edition: 1998 ed.
"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."