# Targeting Bayes factors with direct-path non-equilibrium thermodynamic integration

## TL;DR

This paper introduces a novel thermodynamic integration method that directly targets Bayes factors by avoiding high-variance prior regimes, significantly reducing estimator variance in model comparison tasks.

## Contribution

The authors propose a modified annealing path and non-equilibrium TI approach to improve Bayes factor estimation accuracy and reduce variance compared to existing methods.

## Key findings

- Significant variance reduction in Bayes factor estimates.
- Effective application to Bayesian regression and hierarchical models.
- Improved accuracy over state-of-the-art TI methods.

## Abstract

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.