Fundamentals of Nonparametric Bayesian Inference

Subhashis Ghosal, Aad van der Vaart

• Publisher: Cambridge University Press
• Year: 2017
• Print ISBN:
  9780521878265
• eBook ISBN:
  9781108215527
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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.

Table of contents

• Cover
• Half-title page
• Series page
• Title page
• Copyright page
• Dedication
• Contents
• Expanded Contents
• Glossary of Symbols
• Preface
• 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