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Splitting and merging components of a nonconjugate Dirichlet process mixture model. (English) Zbl 1331.62145

Summary: The inferential problem of associating data to mixture components is difficult when components are nearby or overlapping. We introduce a new split-merge Markov chain Monte Carlo technique that efficiently classifies observations by splitting and merging mixture components of a nonconjugate Dirichlet process mixture model. Our method, which is a Metropolis-Hastings procedure with split-merge proposals, samples clusters of observations simultaneously rather than incrementally assigning observations to mixture components. Split-merge moves are produced by exploiting properties of a restricted Gibbs sampling scan. A simulation study compares the new split-merge technique to a nonconjugate version of Gibbs sampling and an incremental Metropolis-Hastings technique. The results demonstrate the improved performance of the new sampler.

MSC:

62F15 Bayesian inference
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
65C05 Monte Carlo methods
65C40 Numerical analysis or methods applied to Markov chains
62D05 Sampling theory, sample surveys
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