Perfect samplers for mixtures of distributions

Casella, G., Mengersen, K.L., Robert, C.P. and Titterington, D.M. (2002) Perfect samplers for mixtures of distributions. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(4), pp. 777-790. (doi: 10.1111/1467-9868.00360)

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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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Titterington, Professor D
Authors: Casella, G., Mengersen, K.L., Robert, C.P., and Titterington, D.M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Published Online:23 October 2002

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