Perfect Samplers for Mixtures of Distributions
Open Access
- 1 October 2002
- journal article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology
- Vol. 64 (4) , 777-790
- https://doi.org/10.1111/1467-9868.00360
Abstract
Summary: We consider the construction of perfect samplers for posterior distributions associated with mixtures of exponential families and conjugate priors, starting with a perfect slice sampler in the spirit of Mira and co-workers. The methods rely on a marginalization akin to Rao–Blackwellization and illustrate the duality principle of Diebolt and Robert. A first approximation embeds the finite support distribution on the latent variables within a continuous support distribution that is easier to simulate by slice sampling, but we later demonstrate that the approximation can be very poor. We conclude by showing that an alternative perfect sampler based on a single backward chain can be constructed. This alternative can handle much larger sample sizes than the slice sampler first proposed.Funding Information
- National Science Foundation (DMS-9971586)
- Australian Science Council
- Centre National de la Recherche Scientifique
- European Union travel and mobility of researchers network (ERB-FMRX-CT96-0095)
- Statistics Department of the University of Glasgow
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