  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.
