Targeting Bayes factors with direct-path non-equilibrium thermodynamic integration
This work addresses a methodological bottleneck in Bayesian model comparison for researchers in statistics and machine learning, offering an incremental improvement over existing thermodynamic integration techniques.
The authors tackled the high variability in estimating marginal likelihoods via thermodynamic integration, particularly from the prior regime, by proposing a scheme that directly targets log Bayes factors using a modified annealing path between posteriors, combined with non-equilibrium TI to reduce discretisation errors. Results on Bayesian regression models and a hierarchical biopathway model showed a significant reduction in estimator variance compared to state-of-the-art TI methods.
Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a comparatively small number of parameters, intrinsic errors from sampling fluctuations may outweigh the differences in the log marginal likelihood estimates. In the present article, we propose a thermodynamic integration scheme that directly targets the log Bayes factor. The method is based on a modified annealing path between the posterior distributions of the two models compared, which systematically avoids the high variance prior regime. We combine this scheme with the concept of non-equilibrium TI to minimise discretisation errors from numerical integration. Results obtained on Bayesian regression models applied to standard benchmark data, and a complex hierarchical model applied to biopathway inference, demonstrate a significant reduction in estimator variance over state-of-the-art TI methods.