Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Particle filters for mixture models with an unknown number of components.
AU - Fearnhead, Paul
PY - 2004/1
Y1 - 2004/1
N2 - 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.
AB - 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.
KW - Dirichlet process - Gaussian mixture models - Gibbs sampling - MCMC - particle filters
U2 - 10.1023/B:STCO.0000009418.04621.cd
DO - 10.1023/B:STCO.0000009418.04621.cd
M3 - Journal article
VL - 14
SP - 11
EP - 21
JO - Statistics and Computing
JF - Statistics and Computing
SN - 0960-3174
IS - 1
ER -