An Interruptible Algorithm for Perfect Sampling via Markov Chains

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 π 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 long-run distribution π. 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 π. However,...

• Type: Conference
• Year: 1997
• Where: STOC
• Authors: James Allen Fill
• Keywords: Algorithm, Algorithms, Markov Chain Monte Carlo, Markov Chains, STOC 1997