Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics

This book provides a concise summary of statistical inferences with random combinatorial models, especially random partitions and related models, with necessary theoretical backgrounds. Random combinatorial models have been developed at the interface of probability and combinatorics. They are useful for data analyses; however, statistical issues have been raised in each field and a general overview has not been given. This book presents a unified treatment of methods of statistical inferences with random combinatorial models. It begins with an introduction of various kinds of characterizations of Ewens' random partition of an integer and relating important stochastic models, including the Dirichlet process and the coalescent model. Then, statistical issues, such as distributional properties, limit theorems, tests, estimations, Bayesian methods, and Markov chain Monte Carlo issues, are discussed. Carefully chosen examples in various fields, including economics, experimental design, disclosure control, natural languages, physics, and population biology, are presented. This book will appeal to researchers who have an interest in development of statistical methodologies with random combinatorial models and researchers in various fields who are interested in random combinatorial models as statistical tools for data analyses.§