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文章背景与核心概要

本文由 Heinrich von Campe 和 Bjoern Malte Schaefer 撰写，创新性地将马尔可夫链蒙特卡洛（MCMC）循环与热机中的热力学循环过程进行了概念上的类比，用于分析贝叶斯推断问题。作者开发了自适应系综调度器，能够在 MCMC 运行期间调整贝叶斯正则系综的外部参数。

该研究的一项核心理论与实践发现在于：当且仅当底层统计模型为非高斯分布时，这些系统才会产生非零的净功输出。因此，这种热力学方法为衡量贝叶斯推断中的非高斯性提供了一种新颖的定量指标，并通过超新星宇宙学的实证案例进行了验证。

Thermodynamic Cyclic Processes with Markov Samplers in Bayesian Inference

Summary

This paper, authored by Heinrich von Campe and Bjoern Malte Schaefer, introduces the conceptual analogy of Markov chain Monte Carlo (MCMC) cycles to thermodynamic cyclic processes (like those in heat engines) to analyze Bayesian inference problems. The authors develop adaptive ensemble schedulers to tune external parameters of a Bayesian canonical ensemble during MCMC runs. A key theoretical and practical finding of this work is that these systems yield a non-zero net work output if and only if the underlying statistical model is non-Gaussian. Consequently, this thermodynamic approach offers a novel quantitative measure of non-Gaussianity in Bayesian inference, which is demonstrated using an empirical example from supernova cosmology.

Document Details

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 (bothoretically 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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