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Slice sampling mixture models. (English) Zbl 1256.65006

Summary: We propose a more efficient version of the slice sampler for Dirichlet process mixture models described by S. G. Walker [Commun. Stat., Simulation Comput. 36, No. 1, 45–54 (2007; Zbl 1113.62058)]. This new sampler allows for the fitting of infinite mixture models with a wide-range of prior specifications. To illustrate this flexibility we consider priors defined through infinite sequences of independent positive random variables. Two applications are considered: density estimation using mixture models and hazard function estimation. In each case we show how the slice efficient sampler can be applied to make inference in the models. In the mixture case, two submodels are studied in detail. The first one assumes that the positive random variables are gamma distributed and the second assumes that they are inverse-Gaussian distributed. Both priors have two hyperparameters and we consider their effect on the prior distribution of the number of occupied clusters in a sample. Extensive computational comparisons with alternative “conditional” simulation techniques for mixture models using the standard Dirichlet process prior and our new priors are made. The properties of the new priors are illustrated on a density estimation problem.

MSC:

65C50 Other computational problems in probability (MSC2010)
65C05 Monte Carlo methods
65C40 Numerical analysis or methods applied to Markov chains
60J22 Computational methods in Markov chains
60G15 Gaussian processes

Citations:

Zbl 1113.62058
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References:

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