The Annals of Applied Probability

Perfect sampling using bounding chains

Mark Huber

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Bounding chains are a technique that offers three benefits to Markov chain practitioners: a theoretical bound on the mixing time of the chain under restricted conditions, experimental bounds on the mixing time of the chain that are provably accurate and construction of perfect sampling algorithms when used in conjunction with protocols such as coupling from the past. Perfect sampling algorithms generate variates exactly from the target distribution without the need to know the mixing time of a Markov chain at all. We present here the basic theory and use of bounding chains for several chains from the literature, analyzing the running time when possible. We present bounding chains for the transposition chain on permutations, the hard core gas model, proper colorings of a graph, the antiferromagnetic Potts model and sink free orientations of a graph.

Article information

Ann. Appl. Probab. Volume 14, Number 2 (2004), 734-753.

First available in Project Euclid: 23 April 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J22: Computational methods in Markov chains [See also 65C40] 60J27: Continuous-time Markov processes on discrete state spaces 65C05: Monte Carlo methods
Secondary: 65C40: Computational Markov chains 82B80: Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]

Monte Carlo Markov chains perfect simulation coupling from the past mixing times proper colorings Potts model sink free orientations


Huber, Mark. Perfect sampling using bounding chains. Ann. Appl. Probab. 14 (2004), no. 2, 734--753. doi:10.1214/105051604000000080.

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