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

Area of Science:

• Computational statistics
• Bayesian inference
• Model selection

Background:

• Thermodynamic integration (TI) is used for marginal likelihood computation but often suffers from high variance, especially in the prior regime.
• Sampling fluctuations can obscure true differences in log marginal likelihoods when comparing complex models.
• Existing TI methods may not be sufficiently accurate for subtle model differences.

Purpose of the Study:

• To develop a novel TI scheme that directly targets the log Bayes factor for improved accuracy.
• To mitigate the high variance associated with the prior distribution in TI calculations.
• To reduce discretisation errors in numerical integration for more reliable model comparison.

Main Methods:

• A modified annealing path between posterior distributions of compared models is proposed.
• The new path systematically avoids the high-variance prior regime.
• Non-equilibrium TI is integrated to minimize numerical integration errors.

Main Results:

• The proposed TI scheme significantly reduces estimator variance compared to state-of-the-art methods.
• Demonstrated effectiveness on Bayesian regression models and complex hierarchical models for biopathway inference.
• The method provides more stable and reliable log Bayes factor estimates.

Conclusions:

• The novel TI scheme offers a more robust approach for Bayesian model comparison.
• This method enhances the accuracy of comparing complex models, particularly when parameter differences are small.
• The technique is broadly applicable, including in fields like biopathway inference.