Fearnhead, P and Meligkotsidou, L (2007) Filtering Methods for Mixture Models . Journal of Computational and Graphical Statistics, 16 (3). pp. 586-607.
We consider Bayesian inference for mixture distributions of known number of components via a set of filtering recursions. We extend a method - proposed in an earlier article - of direct simulation for discrete mixture distributions in order to analyze continuous mixture models. Furthermore, we introduce resampling steps similar to those in particle filters within the steps of the filtering recursions, which make calculations efficient and enable us to analyze larger datasets. The proposed algorithm for "resampled direct simulation" is a generalization of the particle filter which allows for merging identical/similar particles prior to resampling. We compare the proposed algorithm with this particle filter and with the Gibbs sampler using simulated data and real datasets.
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