Mark Huber Publications

Perfect sampling using bounding chains
The Annals of Applied Probability, M. Huber, vol. 14 no. 2 (August, 2004), pp. 734753.

Abstract: 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.

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

2000 Mathematics Subject Classification: Primary 60J22, 60J27, 65C05; Secondary 65C40, 82B80

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