"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

• Part I: Comparing Partial Orderings Among Stochastic Matrices.- 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 have only Two Columns.- Open Problems.- Part II: Divergence and Contraction Coefficients.- Introduction, Definitions, and Notation.- 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.- Behavior of ϕ ↦ ηϕ (T) for a Fixed Markov Kernel T.- Applications of Global Divergence 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

• Part I: Comparing Partial Orderings Among Stochastic Matrices.- 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 have only Two Columns.- Open Problems.- Part II: Divergence and Contraction Coefficients.- Introduction, Definitions, and Notation.- 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.- Behavior of ϕ ↦ ηϕ (T) for a Fixed Markov Kernel T.- Applications of Global Divergence 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

• Part I: Comparing Partial Orderings Among Stochastic Matrices.- 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 have only Two Columns.- Open Problems.- Part II: Divergence and Contraction Coefficients.- Introduction, Definitions, and Notation.- 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.- Behavior of ϕ ↦ ηϕ (T) for a Fixed Markov Kernel T.- Applications of Global Divergence to Comparison of Experiments.- History of the Problem.