Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics-英文文献.pdf

Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics  James Gary Propp David Bruce Wilson pr oppmathmitedu dbwilsonmitedu Department of Mathematics Massachusetts Institute of Technology Cambridge Massachusetts July Abstract For many applications it is useful to sample from a nite set of ob jects in accordance with some particular distribution One approach is to run an ergo dic ie irreducible ap erio dic Markov chain whose stationary distribution is the desired distribution on this set after the Markov chain has run for M steps with M suciently large the distribution governing the state of the chain approximates the desired distribution Unfortunately it can b e dicult to determine how large M needs to b e We describ e a simple variant of this metho d that determines on its own when to stop and that outputs samples in exact accordance with the desired distribution The metho d uses couplings which have also played a role in other sampling schemes however rather than running the coupled chains from the present into the future one runs from a distant p oint in the past up until the present where the distance into the past that one needs to go is determined during the running of the algorithm itself If the state space has a partial order that is preserved under the moves of the Markov chain then the coupling is often particularly ecient Using our approach one can sample from the Gibbs distributions asso ciated with various st