PreprintCC BY 4.0arXiv
Thermodynamic Cyclic Processes with Markov Samplers in Bayesian Inference
Abstract
The concept of Markov chain Monte Carlo (MCMC) cycles, an analogy to cyclic processes in heat engines, is presented in order to examine Bayesian inference problems. In this effort, we develop adaptive ensemble schedulers that allow the tuning of external parameters of a Bayesian canonical ensemble during an MCMC run, realising the MCMC cycles in practice. We run these cycles on different statistical models. As a fundamental insight, we find (both theoretically and in practice) that such systems can produce a non-zero net work output if and only if the considered model is non-Gaussian. As such, they may serve as a measure of non-Gaussianity in Bayesian inference, which we test on an example from supernova cosmology.
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BibTeX
@misc{campe2026thermodynamic,
title = {{Thermodynamic Cyclic Processes with Markov Samplers in Bayesian Inference}},
author = {Heinrich von Campe and Bjoern Malte Schaefer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07660},
eprint = {2609.07660},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07660},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Thermodynamic Cyclic Processes with Markov Samplers in Bayesian Inference
AU - Heinrich von Campe
AU - Bjoern Malte Schaefer
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07660
UR - https://arxiv.org/abs/2609.07660
AB - The concept of Markov chain Monte Carlo (MCMC) cycles, an analogy to cyclic processes in heat engines, is presented in order to examine Bayesian inference problems. In this effort, we develop adaptive ensemble schedulers that allow the tuning of external parameters of a Bayesian canonical ensemble during an MCMC run, realising the MCMC cycles in practice. We run these cycles on different statistical models. As a fundamental insight, we find (both theoretically and in practice) that such systems can produce a non-zero net work output if and only if the considered model is non-Gaussian. As such, they may serve as a measure of non-Gaussianity in Bayesian inference, which we test on an example from supernova cosmology.
ER -