Fundamentals of Nonparametric Bayesian Inference

Bayesian nonparametrics comes of age with this landmark text synthesizing theory, methodology and computation.

Subhashis Ghosal (Author), Aad van der Vaart (Author)

9780521878265, Cambridge University Press

Hardback, published 26 June 2017

670 pages, 15 b/w illus.
26 x 18.2 x 4 cm, 1.36 kg

'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

Explosive 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 learning, as well as in application areas such as econometrics and biostatistics.

Preface
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.

Subject Areas: Probability & statistics [PBT], Economic statistics [KCHS]