Abstract
Markov Chain Monte-Carlo methods produce a random sample of a given distribution by simulating a Markov chain for which the desired distribution is a reversible measure. In order to generate a sample of size n, we propose to run n independent copies of the chain all starting from the same initial state. If n is large enough, the cutoff phenomenon yields a natural stopping rule. Indeed, the access to equilibrium can be detected using empirical estimates for the expectation of a state function. The method is illustrated by the generation of random samples of stable sets on an undirected graph.
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Ycart, B. Stopping Tests for Markov Chain Monte-Carlo Methods. Methodology and Computing in Applied Probability 2, 23–36 (2000). https://doi.org/10.1023/A:1010003117070
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DOI: https://doi.org/10.1023/A:1010003117070