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Perfect samplers for mixtures of distributions
Author(s) -
Casella G.,
Mengersen K. L.,
Robert C. P.,
Titterington D. M.
Publication year - 2002
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00360
Subject(s) - conjugate prior , prior probability , sampling (signal processing) , distribution (mathematics) , mathematics , sample (material) , exponential function , algorithm , duality (order theory) , exponential distribution , computer science , mathematical optimization , statistics , statistical physics , bayesian probability , combinatorics , mathematical analysis , physics , filter (signal processing) , computer vision , thermodynamics
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.