11. Exact Bayesian Analysis of Mixtures

  1. Kerrie L. Mengersen1,
  2. Christian P. Robert2 and
  3. D. Michael Titterington3
  1. Christian P. Robert2 and
  2. Kerrie L. Mengersen1

Published Online: 24 APR 2011

DOI: 10.1002/9781119995678.ch11

Mixtures: Estimation and Applications

Mixtures: Estimation and Applications

How to Cite

Robert, C. P. and Mengersen, K. L. (2011) Exact Bayesian Analysis of Mixtures, in Mixtures: Estimation and Applications (eds K. L. Mengersen, C. P. Robert and D. M. Titterington), John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119995678.ch11

Editor Information

  1. 1

    School of Mathematical Sciences, Queensland University of Technology, Australia

  2. 2

    Université Paris-Dauphine, CEREMADE, Paris, France

  3. 3

    University of Glasgow, Glasgow, UK

Author Information

  1. 1

    School of Mathematical Sciences, Queensland University of Technology, Australia

  2. 2

    Université Paris-Dauphine, CEREMADE, Paris, France

Publication History

  1. Published Online: 24 APR 2011
  2. Published Print: 15 APR 2011

ISBN Information

Print ISBN: 9781119993896

Online ISBN: 9781119995678

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Keywords:

  • exact Bayesian analysis of mixtures;
  • complete and exact Bayesian analysis - of a parametric mixture model;
  • understanding Bayesian analysis of a mixture model unravels - exploiting missing data structure of model;
  • formal derivation of posterior distribution;
  • conjugate priors, not formally existing - for mixtures of exponential families;
  • true posterior distributions - straightforward derivations, corresponding to completed likelihood;
  • multinomial mixtures;
  • normal mixtures, number of truly different terms - in posterior distribution;
  • Poisson mixture - in the case of a two-component Poisson mixture;
  • number of observations - handled in exact analysis, being extremely limited

Summary

This chapter contains sections titled:

  • Introduction

  • Formal derivation of the posterior distribution

  • References