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Bayesian model comparison relies upon the model evidence, yet for many modelsof interest the model evidence is unavailable in closed form and must beapproximated. Many of the estimators for evidence that have been proposed inthe Monte Carlo literature suffer from high variability. This paper considersthe reduction of variance that can be achieved by exploiting control variatesin this setting. Our methodology is based on thermodynamic integration andapplies whenever the gradient of both the log-likelihood and the log-prior withrespect to the parameters can be efficiently evaluated. Results obtained onregression models and popular benchmark datasets demonstrate a significant andsometimes dramatic reduction in estimator variance and provide insight into thewider applicability of control variates to Bayesian model comparison.

The Controlled Thermodynamic Integral for Bayesian Model Comparison