12. Manifold MCMC for Mixtures

  1. Kerrie L. Mengersen2,
  2. Christian P. Robert3 and
  3. D. Michael Titterington4
  1. Vassilios Stathopoulos and
  2. Mark Girolami

Published Online: 24 APR 2011

DOI: 10.1002/9781119995678.ch12

Mixtures: Estimation and Applications

Mixtures: Estimation and Applications

How to Cite

Stathopoulos, V. and Girolami, M. (2011) Manifold MCMC for 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.ch12

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 Statistical Science, University College London, UK

Publication History

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

ISBN Information

Print ISBN: 9781119993896

Online ISBN: 9781119995678



  • manifold MCMC for mixtures;
  • mixture models, describing a wide variety of random phenomena - because of their inherent flexibility;
  • one problem associated with inefficiency of Gibbs sampler - dependence on a completion;
  • MCMC methods, as the Metropolis adjusted Langevin algorithm (MALA);
  • Markov chain Monte Carlo Methods;
  • Gibbs sampler, simulating individual or subsets of variables - from full conditional distributions;
  • Finite Gaussian mixture models;
  • Gibbs sampler for mixtures of univariate Gaussians;
  • manifold MCMC for mixtures of univariate Gaussians - for MCMC algorithms, reparameterisation of mixture model;
  • application of Riemann manifold Metropolis adjusted Langevin and Hamiltonian Monte Carlo algorithms - on mixtures of univariate Gaussian distributions


This chapter contains sections titled:

  • Introduction

  • Markov chain Monte Carlo Methods

  • Finite Gaussian mixture models

  • Experiments

  • Discussion

  • Acknowledgements

  • Appendix

  • References