Adaptive Model-Switch Thermodynamic Integration: A Bayes Factor Estimator
Abstract
Bayes factors are a widely used model comparison criterion, but are often quite challenging and computationally expensive to estimate well. We propose a variation of the model-switch thermodynamic integration method for estimating Bayes factors that decreases the variance of the estimator and essentially eliminates integration error. We choose samples whose density in β is proportional to the standard deviation of previously drawn samples. Rather than averaging many samples at each β, we use a very dense set of β values, collecting one sample at each in order of increasing β and one sample at each in order of decreasing β to minimize "thermic lag". We study our procedure with a toy model (based loosely on some signal recovery problems). In this model we find that adaptive sampling gives us a 2.7-fold decrease in the spread of the estimated Bayes factor. We test our procedure both drawing directly from the posterior distribution and using a Markov Chain Monte Carlo sampler.
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BibTeX
@misc{malnati2026adaptive,
title = {{Adaptive Model-Switch Thermodynamic Integration: A Bayes Factor Estimator}},
author = {Amanda Malnati and Megan Kralj and Ken D. Olum},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24354},
eprint = {2610.24354},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24354},
}
RIS
TY - UNPB
TI - Adaptive Model-Switch Thermodynamic Integration: A Bayes Factor Estimator
AU - Amanda Malnati
AU - Megan Kralj
AU - Ken D. Olum
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24354
UR - https://arxiv.org/abs/2610.24354
AB - Bayes factors are a widely used model comparison criterion, but are often quite challenging and computationally expensive to estimate well. We propose a variation of the model-switch thermodynamic integration method for estimating Bayes factors that decreases the variance of the estimator and essentially eliminates integration error. We choose samples whose density in β is proportional to the standard deviation of previously drawn samples. Rather than averaging many samples at each β, we use a very dense set of β values, collecting one sample at each in order of increasing β and one sample at each in order of decreasing β to minimize "thermic lag". We study our procedure with a toy model (based loosely on some signal recovery problems). In this model we find that adaptive sampling gives us a 2.7-fold decrease in the spread of the estimated Bayes factor. We test our procedure both drawing directly from the posterior distribution and using a Markov Chain Monte Carlo sampler.
ER -