Prior Processes and Their Applications

Nonparametric Bayesian Estimation

  • Eswar G.¬†Phadia

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Eswar G. Phadia
    Pages 1-108
  3. Eswar G. Phadia
    Pages 109-153
  4. Eswar G. Phadia
    Pages 155-190
  5. Back Matter
    Pages 191-207

About this book

Introduction

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., and discusses their interconnection. In addition, several new processes that have appeared in the literature in recent years and which are off-shoots of the Dirichlet process are described briefly. The second part contains the Bayesian solutions to certain estimation problems pertaining to the distribution function and its functional based on complete data. Because of the conjugacy property of some of these processes, the resulting solutions are mostly in closed form. The third part treats similar problems but based on right censored data. Other applications are also included. A comprehensive list of references is provided in order to help readers explore further on their own.

Keywords

Bayesian nonparametrics Dirichlet process survival function

Authors and affiliations

  • Eswar G.¬†Phadia
    • 1
  1. 1.William Paterson University Department of MathematicsWayneUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-39280-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-39279-5
  • Online ISBN 978-3-642-39280-1
  • About this book
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