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Posterior distributions often feature intractable normalizing constants,called marginal likelihoods or evidence, that are useful for model comparisonvia Bayes factors. This has motivated a number of methods for estimating ratiosof normalizing constants in statistics. In computational physics the logarithmof these ratios correspond to free energy differences. Combining unbiasedMarkov chain Monte Carlo estimators with path sampling, also calledthermodynamic integration, we propose new unbiased estimators of the logarithmof ratios of normalizing constants. As a by-product, we propose unbiasedestimators of the Bayesian cross-validation criterion. The proposed estimatorsare consistent, asymptotically Normal and can easily benefit from parallelprocessing devices. Various examples are considered for illustration.

Unbiased estimation of log normalizing constants with applications to Bayesian cross-validation