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May 2004 Perfect sampling using bounding chains
Mark Huber
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Ann. Appl. Probab. 14(2): 734-753 (May 2004). DOI: 10.1214/105051604000000080


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.


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Mark Huber. "Perfect sampling using bounding chains." Ann. Appl. Probab. 14 (2) 734 - 753, May 2004.


Published: May 2004
First available in Project Euclid: 23 April 2004

zbMATH: 1052.60057
MathSciNet: MR2052900
Digital Object Identifier: 10.1214/105051604000000080

Primary: 60J22 , 60J27 , 65C05
Secondary: 65C40 , 82B80

Keywords: Coupling from the past , Markov chains , Mixing times , Monte Carlo , perfect simulation , Potts model , proper colorings , sink free orientations

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.14 • No. 2 • May 2004
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