Kinetic Theories for Metropolis Monte Carlo Methods

arXiv (Cornell University)

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.

Authors 2

1. Michaël Herty Aachen Institute Geometry and Practical Mathematics

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Institute Geometry and Practical Mathematics , 52056 Aachen , Germany

2. Christian A. Ringhofer

   Arizona State University

   Affiliation as printed

   Arizona State University , School of Mathematical and Statistical Sciences , Tempe , AZ 85287-1804 , USA