Kinetic Theories for Metropolis Monte Carlo Methods

2024/05/02 by Michaël Herty, Herty, Michael, Christian Ringhofer +1
Physics and Astronomy · #35K55 #65C05 #82C22 #Advanced Chemical Physics Studies #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Probability (math.PR) #Theoretical and Computational Physics

paper · doi:10.48550/arxiv.2405.01232

openalex publication_date 2024/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider generalizations of the classical inverse problem to Bayesien type estimators, where the result is not one optimal parameter but an optimal probability distribution in parameter space. The practical computational tool to compute these distributions is the Metropolis Monte Carlo algorithm. We derive kinetic theories for the Metropolis Monte Carlo method in different scaling regimes. The derived equations yield a different point of view on the classical algorithm. It further inspired modifications to exploit the difference scalings shown on an simulation example of the Lorenz system.

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