Fundamentals of Nonparametric Bayesian Inference (Cambridge Series in Statistical and Probabilistic Mathematics)
Cambridge University Press, 6/26/2017
EAN 9780521878265, ISBN10: 0521878268
Hardcover, 670 pages, 26 x 18.2 x 4 cm
Language: English
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.