Markov Chain Monte Carlo Algorithms Allowing Parallel Processing –II
نویسنده
چکیده
A variant of the Metropolis-Rosenbluth-Teller algorithm that allows parallel processing has been described in a previous paper (“Markov Chain Monte Carlo Calculations Allowing Parallel Processing Using a Variant of the Metropolis Algorithm”) that appeared in this journal in 2010. In this follow-on paper, the new algorithm as well as the MetropolisRosenbluth-Teller and Barker algorithms are analyzed for finite, integer-valued Markov Chains, which are easier to understand in detail than continuous variable chains. The new algorithm is shown to approximately satisfy detailed balance when the random walk step is much larger than the support region of the desired steady-state distribution function. Parallelizable versions of the MRT and B algorithms are given. The time to reach a steady state is calculated and compared for these three different algorithms and different number of multiple candidates, potentially offering different degrees of parallel processing.
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