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Target Density Normalization for Markov Chain Monte Carlo Algorithms

Techniques for evaluating the normalization integral of the target density for Markov Chain Monte Carlo algorithms are described and tested numerically. It is assumed that the Markov Chain algorithm has converged to the target distribution and produced a set of samples from the density. These are used to evaluate sample mean, harmonic mean and Laplace algorithms for the calculation of the integral of the target density. A clear preference for the sample mean algorithm applied to a reduced support region is found, and guidelines are given for implementation.