ANALYSING ACCEPTANCE SAMPLING PLANS BY MARKOV CHAINS

On sampling with Markov chains

Markov chains for sampling matchings

Markov Chain Monte Carlo algorithms are often used to sample combinatorial structures such as matchings and independent sets in graphs. A Markov chain is defined whose state space includes the desired sample space, and which has an appropriate stationary distribution. By simulating the chain for a sufficiently large number of steps, we can sample from a distribution arbitrarily close to the sta...

Exact Sampling with Markov Chains

Random sampling has found numerous applications in computer science, statistics, and physics. The most widely applicable method of random sampling is to use a Markov chain whose steady state distribution is the probability distribution r from which we wish to sample. After the Markov chain has been run for long enough, its state is approximately distributed according to 7r. The principal proble...

An Interruptible Algorithm for Perfect Sampling via Markov Chains Short Title: 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 sam...

Sampling Good Motifs with Markov Chains

Markov chain Monte Carlo (MCMC) techniques have been used with some success in bioin­ formatics [LAB93]. However, these results rely on heuristic estimates of a Markov chain’s mixing time. Without provable results, we cannot accurately judge the quality of an algorithm or the output it produces. Our goal is to remedy this situation in the context of the motif­finding problem. Using combinatoria...