13. How many Components in a Finite Mixture?

  1. Kerrie L. Mengersen2,
  2. Christian P. Robert3 and
  3. D. Michael Titterington4
  1. Murray Aitkin

Published Online: 24 APR 2011

DOI: 10.1002/9781119995678.ch13

Mixtures: Estimation and Applications

Mixtures: Estimation and Applications

How to Cite

Aitkin, M. (2011) How many Components in a Finite Mixture?, 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.ch13

Editor Information

  1. 2

    School of Mathematical Sciences, Queensland University of Technology, Australia

  2. 3

    Université Paris-Dauphine, CEREMADE, Paris, France

  3. 4

    University of Glasgow, Glasgow, UK

Author Information

  1. Department of Mathematics and Statistics, University of Melbourne, Australia

Publication History

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

ISBN Information

Print ISBN: 9781119993896

Online ISBN: 9781119995678



  • components in a finite mixture;
  • complexity of prior structures needed for Bayesian analysis - obscurity of their interaction;
  • galaxy data published by Roeder (1990) - recession velocities;
  • normal mixture model;
  • frequentist and Bayesian analyses - straightforward using EM algorithm and Gibbs sampling;
  • Bayesian analyses of data - and choice of priors and their hyperparameters;
  • EW and PS results, supporting strongly models with nine or 10 components - choices of hyperparameter values for MCMC initialisation;
  • posterior distributions of model deviances;
  • asymptotic distributions;
  • posterior deviances - for galaxy data


This chapter contains sections titled:

  • Introduction

  • The galaxy data

  • The normal mixture model

  • Bayesian analyses

  • Posterior distributions for K (for flat prior)

  • Conclusions from the Bayesian analyses

  • Posterior distributions of the model deviances

  • Asymptotic distributions

  • Posterior deviances for the galaxy data

  • Conclusions

  • References