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

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

doi:10.1002/1098-2418(200010/12)17:3/4<290::aid-rsa6>3.0.co;2-q

Cited by 58 publications

(27 citation statements)

References 42 publications

(93 reference statements)

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“…(N ; c) is a monotone chain, we can design a perfect sampler based on monotone CFTP. We could also have employed Wilson's read once algorithm (Wilson 2000) or Fill's interruptible algorithm (Fill 1998;Fill et al 2000), each of which also yields a perfect sampler.…”

Section: Theorem 42 the Markov Chain M Pmentioning

confidence: 97%

Randomized approximation scheme and perfect sampler for closed Jackson networks with multiple servers

Kijima

Matsui

2008

Ann Oper Res

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In this paper, we propose a fully polynomial-time randomized approximation scheme (FPRAS) for a closed Jackson network. Our algorithm is based on the Markov chain Monte Carlo (MCMC) method. Thus our scheme returns an approximate solution, for which the size of the error satisfies a given bound. To our knowledge, this algorithm is the first polynomial time MCMC algorithm for closed Jackson networks with multiple servers. We propose two new ergodic Markov chains, both of which have a unique stationary distribution that is the product form solution for closed Jackson networks. One of them is for an approximate sampler, and we show that it mixes rapidly. The other is for a perfect sampler based on the monotone coupling from the past (CFTP) algorithm proposed by Propp and Wilson, and we show that it has a monotone update function.

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Section: Theorem 42 the Markov Chain M Pmentioning

confidence: 97%

Randomized approximation scheme and perfect sampler for closed Jackson networks with multiple servers

Kijima

Matsui

2008

Ann Oper Res

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“…The CFTP algorithm is only practical for small discrete sample spaces or for a target distribution having a probability space equipped with a partial order preserved by an appropriate Markov chain construction. Although in recent decades, there have been many theoretical developments and applications in this area 1350-7265 © 2017 ISI/BS such as [4,8,15,16,20,24,28] and [9], the CFTP algorithm is still not practical for complex statistical models.…”

Section: Background Of Exact Monte Carlo Simulationmentioning

confidence: 99%

A new rejection sampling method without using hat function

Dai¹

2017

Bernoulli

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This paper proposes a new exact simulation method, which simulates a realisation from a proposal density and then uses exact simulation of a Langevin diffusion to check whether the proposal should be accepted or rejected. Comparing to the existing coupling from the past method, the new method does not require constructing fast coalescence Markov chains. Comparing to the existing rejection sampling method, the new method does not require the proposal density function to bound the target density function. The new method is much more efficient than existing methods for certain problems. An application on exact simulation of the posterior of finite mixture models is presented.

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“…In the present paper, the authors extend the results of Strassen, Kamae, Krengel and O'Brien to pairs of Markov kernels on ordered Polish spaces. The original motivation for our work stemmed from the desire to establish a general result guaranteeing the existence of an upward coupler that plays a key role in Fill's perfect rejection sampling algorithm [4]. While the existence of such a coupler in the case of a countable probability space is an easy exercise, the case of an uncountable Polish space requires some care, as explained below.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 3 we prove the existence of an upward coupler in the case when k is stochastically dominated by k , which plays a key role in Fill's perfect rejection sampling algorithm (Section 7.2 of [4]). The following short argument will help to illustrate the importance of M.…”

Section: Introductionmentioning

confidence: 99%

Monotone bivariate Markov kernels with specified marginals

Machida

Shibakov

2010

Proc. Amer. Math. Soc.

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Abstract. Given two Markov kernels k and k on an ordered Polish space, such that k is stochastically dominated by k , we establish the existence of: (i) a monotone bivariate Markov kernel whose marginals are k and k and (ii) an upward coupler from k to k . This extends the results of Strassen, Kamae, Krengel and O'Brien to Markov kernels. Two examples are also given. The first is a simple illustration of our original motivation for this work, while the second demonstrates the optimality of our main result. The key technique is a combination of the standard probability/charge approach and the use of measurable selections of multivalued measurable maps.

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

Cited by 58 publications

References 42 publications

Randomized approximation scheme and perfect sampler for closed Jackson networks with multiple servers

Randomized approximation scheme and perfect sampler for closed Jackson networks with multiple servers

A new rejection sampling method without using hat function

Monotone bivariate Markov kernels with specified marginals

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