Description
Book SynopsisExplosive growth in computing power has made Bayesian methods for infinite-dimensional models - Bayesian nonparametrics - a nearly universal framework for inference, finding practical use in numerous subject areas. Written by leading researchers, this authoritative text draws on theoretical advances of the past twenty years to synthesize all aspects of Bayesian nonparametrics, from prior construction to computation and large sample behavior of posteriors. Because understanding the behavior of posteriors is critical to selecting priors that work, the large sample theory is developed systematically, illustrated by various examples of model and prior combinations. Precise sufficient conditions are given, with complete proofs, that ensure desirable posterior properties and behavior. Each chapter ends with historical notes and numerous exercises to deepen and consolidate the reader's understanding, making the book valuable for both graduate students and researchers in statistics and machine
Trade Review'Probabilistic inference of massive and complex data has received much attention in statistics and machine learning, and Bayesian nonparametrics is one of the core tools. Fundamentals of Nonparametric Bayesian Inference is the first book to comprehensively cover models, methods, and theories of Bayesian nonparametrics. Readers can learn basic ideas and intuitions as well as rigorous treatments of underlying theories and computations from this wonderful book.' Yongdai Kim, Seoul National University
'Bayesian nonparametrics has seen amazing theoretical, methodological, and computational developments in recent years. This timely book gives an authoritative account of the current state of the art by two leading scholars in the field. They masterfully cover all major aspects of the discipline, with an emphasis on asymptotics, and achieve the rare feat of being simultaneously broad and deep, while preserving the utmost mathematical rigor. This book is, without doubt, a must-read for Ph.D. students and researchers in statistics and probability.' Igor Prünster, Università Commerciale Luigi Bocconi, Milan
'Worth waiting for, this book gives a both global and precise overview on the fundamentals of Bayesian nonparametrics. It will be extremely valuable as a textbook for Masters and Ph.D. students, along with more experienced researchers, as the authors have managed to gather, link together, and present with great clarity a large part of the major advances in Bayesian nonparametric modeling and theory.' Judith Rousseau, Université Paris-Dauphine
'This book can serve as a textbook for a graduate course on Bayesian nonparametrics. It can also be used as a reference book for researchers in both statistics and machine learning, as well as application areas such as econometrics and biostatistics.' Yuehua Wu, MathSciNet
Table of ContentsPreface; Glossary of symbols; 1. Introduction; 2. Priors on function spaces; 3. Priors on spaces of probability measures; 4. Dirichlet processes; 5. Dirichlet process mixtures; 6. Consistency: general theory; 7. Consistency: examples; 8. Contraction rates: general theory; 9. Contraction rates: examples; 10. Adaptation and model selection; 11. Gaussian process priors; 12. Infinite-dimensional Bernstein–von Mises theorem; 13. Survival analysis; 14. Discrete random structures; Appendices; References; Author index; Subject index.
