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The Poisson-Dirichlet Distribution and Related Topics

Models and Asymptotic Behaviors

  • Shui Feng

Part of the Probability and its Applications book series (PIA)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Models

    1. Front Matter
      Pages 1-1
    2. Shui Feng
      Pages 3-14
    3. Shui Feng
      Pages 15-52
    4. Shui Feng
      Pages 67-80
    5. Shui Feng
      Pages 81-112
    6. Shui Feng
      Pages 113-124
  3. Asymptotic Behaviors

    1. Front Matter
      Pages 125-125
    2. Shui Feng
      Pages 127-150
  4. Back Matter
    Pages 199-218

About this book

Introduction

The Poisson-Dirichlet distribution is an infinite dimensional probability distribution. It was introduced by Kingman over thirty years ago, and has found applications in a broad range of areas including Bayesian statistics, combinatorics, differential geometry, economics, number theory, physics, and population genetics. This monograph provides a comprehensive study of this distribution and some related topics, with particular emphasis on recent progresses in evolutionary dynamics and asymptotic behaviors. One central scheme is the unification of the Poisson-Dirichlet distribution, the urn structure, the coalescent, the evolutionary dynamics through the grand particle system of Donnelly and Kurtz. It is largely self-contained. The methods and techniques used in it appeal to researchers in a wide variety of subjects.

Keywords

Coalescent Dirichlet process Limit theorems Measure Poisson process Poisson-Dirichlet Distribution Population Genetics Probability and stochastic processes Probability distribution random measure

Authors and affiliations

  • Shui Feng
    • 1
  1. 1.Dept. Mathematics & StatisticsMcMaster UniversityHamiltonCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-11194-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-11193-8
  • Online ISBN 978-3-642-11194-5
  • Series Print ISSN 1431-7028
  • Buy this book on publisher's site