Exact Sampling with Markov Chains
Year: 1996
Type: article
Abstract: 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 ß from which we wish to sample. After the Markov chain has been run for long enough, its state is approximately distributed according to ß. The principal problem with this approach is that it is often difficult to determine how long to run the Markov chain. In this thesis we present several algorithms that use Markov chains to return samples distributed exactly according to ß. The algorithms determine on their own how long to run the Markov chain. Two of the algorithms may be used with any Markov chain, but are useful only if the state space is not too large. Nonetheless, a spin-off of these two algorithms is a procedure for sampling random spanning trees of a directed graph that runs more quickly than the Aldous/Broder algorithm. Another of the exact sa...
Author: David Bruce Wilson
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1533143729