We propose a more efficient version of the slice sampler for Dirichlet process mixture models described by Walker (Commun. Stat., Simul. Comput. 36:45–54, 2007). 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.
KeywordsDirichlet process Markov chain Monte Carlo Mixture model Normalized weights Slice sampler Hazard function
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- Dunson, D.: Kernel local partition processes for functional data. Discussion paper 2008-26, Department of Statistical Science, Duke University (2008) Google Scholar
- Escobar, M.D.: Estimating the means of several normal populations by nonparametric estimation of the distribution of the means. Unpublished Ph.D. dissertation, Department of Statistics, Yale University (1988) Google Scholar
- Papaspiliopoulos, O.: A note on posterior sampling from Dirichlet mixture models. Preprint (2008) Google Scholar
- Sokal, A.: Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms Functional Integration, Cargése, 1996. NATO Adv. Sci. Inst. Ser. B Phys., vol. 361, pp. 131–192. Plenum, New York (1997), Google Scholar
- Van Gael, J., Saatchi, Y., Teh, Y.W., Ghahramani, Z.: Beam sampling for the infinite hidden Markov model. Technical Report: Engineering Department, University of Cambridge (2008) Google Scholar
- Yau, C., Papaspiliopoulos, O., Roberts, G.O., Holmes, C.: Bayesian nonparametric hidden Markov models with application to the analysis of copy-number-variation in mammalian genomes. Technical Report, Man Institute, Oxford (2008) Google Scholar