Statistics and Computing

, Volume 14, Issue 1, pp 11–21

Particle filters for mixture models with an unknown number of components

  • Paul Fearnhead

DOI: 10.1023/

Cite this article as:
Fearnhead, P. Statistics and Computing (2004) 14: 11. doi:10.1023/


We consider the analysis of data under mixture models where the number of components in the mixture is unknown. We concentrate on mixture Dirichlet process models, and in particular we consider such models under conjugate priors. This conjugacy enables us to integrate out many of the parameters in the model, and to discretize the posterior distribution. Particle filters are particularly well suited to such discrete problems, and we propose the use of the particle filter of Fearnhead and Clifford for this problem. The performance of this particle filter, when analyzing both simulated and real data from a Gaussian mixture model, is uniformly better than the particle filter algorithm of Chen and Liu. In many situations it outperforms a Gibbs Sampler. We also show how models without the required amount of conjugacy can be efficiently analyzed by the same particle filter algorithm.

Dirichlet processGaussian mixture modelsGibbs samplingMCMCparticle filters

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Paul Fearnhead
    • 1
  1. 1.Department of Mathematics and StatisticsLancaster UniversityLancaster