Prior processes and their applications : nonparametric bayesian estimation / Eswar G. Phadia.

Includes bibliographical references and index.

Prior Processes and Their Applications; Preface; Acknowledgements;
Contents:
Chapter 1: Prior Processes
1.1 Prior Processes-An Overview
1.1.1 Introduction
1.1.2 Methods of Construction
1.1.3 Prior Processes
1.2 Dirichlet Process
1.2.1 Definition
1.2.2 Properties
1.3 Dirichlet Invariant Process
1.3.1 Definition
1.3.2 Properties
1.3.3 Symmetrized Dirichlet Process
1.4 Mixtures of Dirichlet Processes
1.4.1 Definition
1.4.2 Properties
1.5 Processes Neutral to the Right
1.5.1 Definition
1.5.2 Properties
1.5.3 Non-decreasing Processes with Independent Increments 1.5.4 Alternate Representation of the Neutral to the Right Process
1.5.5 Posterior Distribution
1.6 Gamma Process
1.6.1 Definition
1.6.2 Posterior Distribution
1.7 Extended Gamma Process
1.7.1 Definition
1.7.2 Properties
1.7.3 Posterior Distribution
1.8 Beta Processes
1.8.1 Definition
1.8.2 Properties
1.8.3 Posterior Distribution
1.8.4 Hierarchical Beta Process
1.9 Beta-Stacy Process
1.9.1 Definition
1.9.2 Properties
1.9.3 Posterior Distribution
1.10 Tailfree Processes
1.10.1 Definition
1.10.2 The Dyadic Tailfree Process
1.10.3 Properties
1.11 Polya Tree Processes
1.11.1 Definition
1.11.2 Properties
1.12 Ferguson-Sethuraman Processes. Multiplicities in a Sample
1.12.1 Discrete and Finite Dimensional Priors
1.12.2 Beta Two-Parameter Process
1.12.3 Dependent and Spatial Dirichlet Processes
1.12.4 Kernel Based Stick-Breaking Processes
1.13 Poisson-Dirichlet Processes
1.13.1 One-Parameter Poisson-Dirichlet Process
1.13.2 Two-Parameter Poisson-Dirichlet Process
1.14 Chinese Restaurant and Indian Buffet Processes
1.14.1 Chinese Restaurant Process
1.14.2 Indian Buffet Process
1.15 Some Other Processes
1.15.1 Dirichlet-Multinomial Process
1.15.2 Dirichlet Multivariate Process
1.15.3 Generalized Dirichlet Process
1.15.4 Beta-Neutral Process
1.15.5 Bernstein-Dirichlet Prior
1.15.6 Hierarchical and Mixture Processes
1.16 Bivariate Processes
1.16.1 Bivariate Tailfree Process
Chapter 2: Inference Based on Complete Data
2.1 Introduction
2.2 Estimation of a Distribution Function
2.2.1 Estimation of a CDF
2.2.2 Estimation of a Symmetric CDF
2.2.3 Estimation of a CDF with MDP Prior
3. Inference Based on Incomplete Data
3.1 Introduction
3.2 Estimation of a SF Based on DP Priors
3.3 Estimation of a SF Based on Other Priors
3.4 Linear Bayes Estimation of a SF
3.5 Other Estimation Problems
3.6 Hypothesis Testing Ho: F<= G
3.7 Estimation in Presence of Covariates
References
Author Index
Subject Index

This book presents a systematic and comprehensive treatment of various prior processes that have been developed over the last four decades in order to deal with the Bayesian approach to solving some nonparametric inference problems. Applications of these priors in various estimation problems are presented. Starting with the famous Dirichlet process and its variants, the first part describes processes neutral to the right, gamma and extended gamma, beta and beta-Stacy, tail free and Polya tree, one and two parameter Poisson-Dirichlet, the Chinese Restaurant and Indian Buffet processes, etc., an.