# The Controlled Thermodynamic Integral for Bayesian Model Comparison

arXiv: https://arxiv.org/abs/1404.5053 · HTML: https://mlsanity.com/paper/1404.5053/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2014.

## Built on by (most cited first, 2 of 2)

- [Meta-learning Control Variates: Variance Reduction with Limited Data](https://mlsanity.com/paper/2303.04756/) (2023)
- [Bayesian Numerical Integration with Neural Networks](https://mlsanity.com/paper/2305.13248/) (2023)

## Abstract (arXiv)

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