Direct simulation for discrete mixture distributions

Authors:
Paul Fearnhead
Affiliations:
Department of Mathematics and Statistics, Lancaster University, UK
Venue:
Statistics and Computing
Year:
2005

Citing 3
Cited 2

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Bayesian learning of finite generalized inverted Dirichlet mixtures: Application to object classification and forgery detection

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Abstract

We demonstrate how to perform direct simulation for discrete mixture models. The approach is based on directly calculating the posterior distribution using a set of recursions which are similar to those of the Forward-Backward algorithm. Our approach is more practicable than existing perfect simulation methods for mixtures. For example, we analyse 1096 observations from a 2 component Poisson mixture, and 240 observations under a 3 component Poisson mixture (with unknown mixture proportions and Poisson means in each case). Simulating samples of 10,000 perfect realisations took about 17 minutes and an hour respectively on a 900 MHz ultraSPARC computer. Our method can also be used to perform perfect simulation from Markov-dependent mixture models. A byproduct of our approach is that the evidence of our assumed models can be calculated, which enables different models to be compared.