2004/05/01 by Mark Huber · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Markov Chains and Monte Carlo Methods #Protein Structure and Dynamics #math.PR #msc:60J22 #msc:60J27 #msc:65C05 #msc:65C40 #msc:82B80
paper · pdf · doi:10.1214/105051604000000080
published as Annals of Applied Probability 2004, Vol. 14, No. 2, 734-753
openalex publication_date 2004/05/01 · arxiv created 2004/05/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.