Multidimensional Integration of a Positive Function Using Markov Chain Monte Carlo
نویسنده
چکیده
A new Markov Chain Monte Carlo 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 second follow-on paper, the problem of calculating the normalization integral of the distribution function is considered. In the usual Markov Chain Monte Carlo calculations this normalization integral is not necessary; however, this integral is needed for Bayesian hypothesis testing and is a key quantity (the partition function) in statistical physics. Three different methods of calculating this integral are considered: an importance-sampling method, a reference-hypothesis method, and a direct method of integration over the random-walk region. This latter method is shown to provide the normalization integral in situations where the other methods fail.
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