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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1999-25
August 1999

Perfect simulation for sample-based inference


Jesper Møller

Geoff K. Nicholls


Perfect simulation algorithms based on Propp and Wilson (1996) have so far been of limited use for sampling problems of interest in statistics. We spe cify a new family of perfect sampling algorithms obtained by combining MCMC tempering algorithms with dominated coupling from the past, and demonstrate that our algorithms will be useful for sample based inference. Perfect tempering algorithms are less efficient than the MCMC algorithms on which they typically depend. However, samples returned by perfect tempering are distributed according to the intended distribution, so that these new sampling algorithms do not suffer from the convergence problems of MCMC. Perfect tempering is related to rejection sampling. When rejection sampling has been tried, but has proved impractical, it may be possible to convert the rejection algorithm into a perfect tempering algorithm, with a significant gain in algorithm efficiency.

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This paper has now been published in Conditionally accepted for Statistics and Computing