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44
An Interruptible Algorithm for Perfect Sampling via Markov Chains
 Annals of Applied Probability
, 1998
"... For a large class of examples arising in statistical physics known as attractive spin systems (e.g., the Ising model), one seeks to sample from a probability distribution # on an enormously large state space, but elementary sampling is ruled out by the infeasibility of calculating an appropriate nor ..."
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Cited by 92 (7 self)
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For a large class of examples arising in statistical physics known as attractive spin systems (e.g., the Ising model), one seeks to sample from a probability distribution # on an enormously large state space, but elementary sampling is ruled out by the infeasibility of calculating an appropriate normalizing constant. The same difficulty arises in computer science problems where one seeks to sample randomly from a large finite distributive lattice whose precise size cannot be ascertained in any reasonable amount of time. The Markov chain Monte Carlo (MCMC) approximate sampling approach to such a problem is to construct and run "for a long time" a Markov chain with longrun distribution #. But determining how long is long enough to get a good approximation can be both analytically and empirically difficult. Recently, Jim Propp and David Wilson have devised an ingenious and efficient algorithm to use the same Markov chains to produce perfect (i.e., exact) samples from #. However, the running t...
An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants
 Biometrika
, 2006
"... Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method i ..."
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Cited by 86 (3 self)
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Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value. The proposal distribution is constructed so that the normalising constant cancels from the Metropolis–Hastings ratio. The method is illustrated by producing posterior samples for parameters of the Ising model given a particular lattice realisation.
Exact sampling for Bayesian inference: towards general purpose algorithms
 Bayesian Statistics 6
, 1998
"... this paper are fairly easy to implement and could be used as diagnostics instead. Nonexact uses of couplers are also discussed in Murdoch and Rosenthal (1998). Regarding Professor Tierney's ideas for a use for noncoalesced endpoints: unfortunately, we do not have a coupler that is both genera ..."
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Cited by 48 (6 self)
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this paper are fairly easy to implement and could be used as diagnostics instead. Nonexact uses of couplers are also discussed in Murdoch and Rosenthal (1998). Regarding Professor Tierney's ideas for a use for noncoalesced endpoints: unfortunately, we do not have a coupler that is both general purpose and easy to apply, where it is straightforward to come up with a finite list of candidates from an easily identifiable time. The rejection and multigamma couplers are too hard to apply, and the random walk couplers can have infinite sets of states that take a long time to move. Finally, we know this is a Bayesian conference and a Bayesian volume, but we still think it is entirely appropriate to take a frequentist perspective in judging the quality of a Monte Carlo sample!
Extension of Fill’s perfect rejection sampling algorithm to general chains (extended abstract
 Pages 37–52 in Monte Carlo Methods
, 2000
"... 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 th ..."
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Cited by 47 (14 self)
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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. Key words and phrases. Fill’s algorithm, Markov chain Monte Carlo, perfect sampling, exact sampling, rejection sampling, interruptibility, coupling from the past, readonce coupling from the past, monotone transition rule, realizable monotonicity, stochastic monotonicity, partially ordered set, coalescence, imputation,
How to Couple from the Past Using a ReadOnce Source of Randomness
, 1999
"... We give a new method for generating perfectly random samples from the stationary distribution of a Markov chain. The method is related to coupling from the past (CFTP), but only runs the Markov chain forwards in time, and never restarts it at previous times in the past. The method is also related ..."
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Cited by 40 (1 self)
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We give a new method for generating perfectly random samples from the stationary distribution of a Markov chain. The method is related to coupling from the past (CFTP), but only runs the Markov chain forwards in time, and never restarts it at previous times in the past. The method is also related to an idea known as PASTA (Poisson arrivals see time averages) in the operations research literature. Because the new algorithm can be run using a readonce stream of randomness, we call it readonce CFTP. The memory and time requirements of readonce CFTP are on par with the requirements of the usual form of CFTP, and for a variety of applications the requirements may be noticeably less. Some perfect sampling algorithms for point processes are based on an extension of CFTP known as coupling into and from the past; for completeness, we give a readonce version of coupling into and from the past, but it remains unpractical. For these point process applications, we give an alternative...
Perfect simulation of conditionally specified models
, 1999
"... . JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the ..."
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Cited by 38 (4 self)
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. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
Exact Sampling and Approximate Counting Techniques
"... We present two algorithms for uniformly sampling from the proper colorings of a graph using k colors. We use exact sampling from the stationary distribution of a Markov chain with states that are the kcolorings of a graph with maximum degree ¢. As opposed to approximate sampling algorithms based on ..."
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Cited by 35 (10 self)
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We present two algorithms for uniformly sampling from the proper colorings of a graph using k colors. We use exact sampling from the stationary distribution of a Markov chain with states that are the kcolorings of a graph with maximum degree ¢. As opposed to approximate sampling algorithms based on rapid mixing, these algorithms have termination criteria that allow them to stop on some inputs much more quickly than in the worst case running time bound. For the first algorithm we show that when ¡¤£, the algorithm has an upper limit on the expected running time that is polynomial. For the second algorithm we show that for ¡�£�� where ¢� � � is an integer that satisfies ����£�� the running time is polynomial. Previously, Jerrum showed that it was possible to approximately sample uniformly in polynomial time from the set of ¡colorings when ¡�� but our algorithm is the first polynomial time exact sampling algorithm for this problem. Using approximate sampling, Jerrum also showed how to approximately count the number of ¡colorings. We give a new procedure for approximately counting the number of ¡colorings that improves the running time of the procedure of Jerrum by a factor of is the number of nodes in �� � when ¥����, where �� ¢ � the graph to be colored � and is the number of edges. In addition, we present an improved analysis of the chain of Luby and Vigoda for exact sampling from the independent sets of a graph. Finally, we present the first polynomial time method for exactly sampling from the sink free orientations of a graph. Bubley and Dyer showed how to approximately sample from this state space ��¥���������¥��������� � in time, our algorithm ��¥��¦�� � takes expected time.
Coupling from the Past: a User's Guide
, 1997
"... . The Markov chain Monte Carlo method is a general technique for obtaining samples from a probability distribution. In earlier work, we showed that for many applications one can modify the Markov chain Monte Carlo method so as to remove all bias in the output resulting from the biased choice of an i ..."
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Cited by 30 (2 self)
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. The Markov chain Monte Carlo method is a general technique for obtaining samples from a probability distribution. In earlier work, we showed that for many applications one can modify the Markov chain Monte Carlo method so as to remove all bias in the output resulting from the biased choice of an initial state for the chain; we have called this method Coupling From The Past (CFTP). Here we describe this method in a fashion that should make our ideas accessible to researchers from diverse areas. Our expository strategy is to avoid proofs and focus on sample applications. 1. Introduction In Markov chain Monte Carlo studies, one attempts to sample from a distribution ß by running a Markov chain whose unique steadystate distribution is ß. Ideally, one has proved a theorem that guarantees that the time for which one plans to run the chain is substantially greater than the mixing time of the chain, so that the distribution ~ ß that one's procedure actually samples from is known to be cl...
MULTIPROCESS PARALLEL ANTITHETIC COUPLING FOR BACKWARD AND FORWARD Markov Chain Monte Carlo
, 2005
"... Antithetic coupling is a general stratification strategy for reducing Monte Carlo variance without increasing the simulation size. The use of the antithetic principle in the Monte Carlo literature typically employs two strata via antithetic quantile coupling. We demonstrate here that further stratif ..."
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Cited by 28 (10 self)
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Antithetic coupling is a general stratification strategy for reducing Monte Carlo variance without increasing the simulation size. The use of the antithetic principle in the Monte Carlo literature typically employs two strata via antithetic quantile coupling. We demonstrate here that further stratification, obtained by using k>2(e.g.,k = 3–10) antithetically coupled variates, can offer substantial additional gain in Monte Carlo efficiency, in terms of both variance and bias. The reason for reduced bias is that antithetically coupled chains can provide a more dispersed search of the state space than multiple independent chains. The emerging area of perfect simulation provides a perfect setting for implementing the kprocess parallel antithetic coupling for MCMC because, without antithetic coupling, this class of methods delivers genuine independent draws. Furthermore, antithetic backward coupling provides a very convenient theoretical tool for investigating antithetic forward coupling. However, the generation of k>2 antithetic variates that are negatively associated, that is, they preserve negative correlation under monotone
On exact simulation of Markov random fields using coupling from the past
, 1997
"... A general framework for exact simulation of Markov random fields using the ProppWilson coupling from the past approach is proposed. Our emphasis is on situations lacking the monotonicity properties that have been exploited in previous studies. A critical aspect is the convergence time of the algori ..."
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Cited by 22 (2 self)
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A general framework for exact simulation of Markov random fields using the ProppWilson coupling from the past approach is proposed. Our emphasis is on situations lacking the monotonicity properties that have been exploited in previous studies. A critical aspect is the convergence time of the algorithm; this we study both theoretically and experimentically.