Extension of Fill’s perfect rejection sampling algorithm to general chains (Extended abstract)

Fill, James Allen; Machida, Motoya; Murdoch, Duncan J.; Rosenthal, Jeffrey S.

doi:10.1090/fic/026/03

Cited by 3 publications

(1 citation statement)

References 7 publications

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“…(b) This algorithm is, like Fill's original algorithm [11], a form of rejection sampling (see, e.g., Devroye [6]). This is explained in Section 2 of [14].…”

Section: Remark 22mentioning

confidence: 99%

Extension of Fill's perfect rejection sampling algorithm to general chains

Fill

Machida

Murdoch

et al. 2000

Random Struct. Alg.

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By developing and applying a broad framework for rejection sampling using auxiliary randomness, we provide an extension of the perfect sampling algorithm of Fill (1998) to general chains on quite general state spaces, and describe how use of bounding processes can ease computational burden. Along the way, we unearth a simple connection between the Coupling From The Past (CFTP) algorithm originated by Propp and Wilson (1996) and our extension of Fill's algorithm.

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“…(b) This algorithm is, like Fill's original algorithm [11], a form of rejection sampling (see, e.g., Devroye [6]). This is explained in Section 2 of [14].…”

Section: Remark 22mentioning

confidence: 99%

Extension of Fill's perfect rejection sampling algorithm to general chains

Fill

Machida

Murdoch

et al. 2000

Random Struct. Alg.

Self Cite

View full text Add to dashboard Cite

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A Primer on Perfect Simulation

Thönnes¹

Statistical Physics and Spatial Statistics

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A Guide to Exact Simulation

Dimakos

2001

Int Statistical Rev

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Markov Chain Monte Carlo (MCMC) methods are used to sample from complicated multivariate distributions with normalizing constants that may not be computable in practice and from which direet sampling is not feasible. A fundamental problem is to determine convergence of the chains. Propp & Wilson (1996) devised a Markov chain algorithm called Coupling From The Past (CFTP) that solves this problem, as it produces exact samples from the target distribution and determines automatidy how long it needs to run. Exact sampling by CF"P and other methods is currently a thriving resuuch topic. This paper gives a review of some of thee ideas, with emphasis on the CFI'P dgorith. The concepts of coupling and monotone CFTP are introduced, and results on the running time of the algorithm presented. The interruptible method of F i l l (1998) and the method of Murdoch & Green (1998) for exact sampling for continuous distributions are presented. Novel simulation experiments are reported for exact sampling from the Ising model in the setting of Bayesian image restoration, and the results are compared to standard MCMC. The results show that C F " worka at least as well as standard MCMC, with convergence monitored by the method d M e r y & Lewis (19!E, 199a).

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Extension of Fill’s perfect rejection sampling algorithm to general chains (Extended abstract)

Cited by 3 publications

References 7 publications

Extension of Fill's perfect rejection sampling algorithm to general chains

Extension of Fill's perfect rejection sampling algorithm to general chains

A Primer on Perfect Simulation

A Guide to Exact Simulation

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