Abstract
The Bayes factor is a useful summary for model selection. Calculation of this measure involves evaluating the integrated likelihood (or prior predictive density), which can be estimated from the output of MCMC and other posterior simulation methods using the harmonic mean estimator. vVhile this is a simulation-consistent estimator, it can have infinite variance. In this article we describe a method to stabilize the harmonic mean estimator. Under this approach, the parameter space is reduced such that the modified estimator involves a harmonic mean of heavier tailed densities, thus resulting in a finite variance estimator. We discuss general conditions under which this reduction is applicable and illustrate the proposed method through several examples. Bayes factor, Beta-binomial, Integrated likelihood, Poisson-Gamma distribution, Statistical Variance reduction.
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