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MCMC for Normalized Random Measure Mixture Models
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DOI：10.1214/13-STS422.png)
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Abstract
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This paper concerns the use of Markov chain Monte Carlo methods for posterior sampling in Bayesian nonparametric mixture models with normalized random measure priors. Making use of some recent posterior characterizations for the class of normalized random measures, we propose novel Markov chain Monte Carlo methods of both marginal type and conditional type. The proposed marginal samplers are generalizations of Neal's well-regarded Algorithm 8 for Dirichlet process mixture models, whereas the conditional sampler is a variation of those recently introduced in the literature. For both the marginal and conditional methods, we consider as a running example a mixture model with an underlying normalized generalized Gamma process prior, and describe comparative simulation results demonstrating the efficacies of the proposed methods.
Keywords:
Bayesian nonparametrics
hierarchical mixture model
completely random measure
normalized random measure
Dirichlet process
noimalized generalized Gamma process
MCMC posterior sampling method
marginalized sampler
Algorithm 8
conditional sampler
slice sampling
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