Nonparametric Bayesian inference. (Q2871942)

``Bayesian nonparametric (BNP) inference allows us to acknowledge uncertainty about an assumed model while maintaining a practically feasible inference approach.'' The focus of this book, that originates from the notes of a short course given at UC Santa Cruz in summer 2010, is on BNP models for random probability measures (RPMs). The authors provide a rather comprehensive picture with the aim of putting the recent proliferation of models into some perspective and of clarifying the relationships between commonly adopted BNP models. The Dirichlet process (DP) is arguably the most popular BNP model for RPMs and has a central role in this book as it arises as a special case of several other models. Among the possible generalizations of the DP, particular attention is dedicated to Pólya trees, species sampling models and dependent Dirichlet processes. While an introductory chapter is dedicated to the illustration of typical applications of BNP models to data analysis, overall the emphasis of the book is on the development of models rather than on their application to statistical inference problems. Posterior simulation schemes for DP and DP mixture models are also discussed.