TABLE OF CONTENTS Bernd A.Berg
Department of Physics
Florida State University
Tallahassee, Florida 32306 4350, USA
and
School of Computational Science
Florida State University
Tallahassee, Florida 32306 4120, USA
E-mail: berg@csit.fsu.edu
This article is a tutorial on Markov chain Monte Carlo simulations and their statistical analysis. The theoretical concepts are illustrated through many numerical assignments from the author s book [7] on the subject. Computer code (in Fortran) is available for all subjects covered and can be downloaded from the web.
Markov chain Monte Carlo (MC) simulations started in earnest with the 1953 article by Nicholas Metropolis, Arianna Rosenbluth, Marshall Rosenbluth, Augusta Teller and Edward Teller [18]. Since then MC simulations have become an indispensable tool with applications in many branches of science. Some of those are reviewed in the proceedings [13] of the 2003 Los Alamos conference, which celebrated the 50th birthday of Metropolis simulations.
The purpose of this tutorial is to provide an overview of basic concepts, which are prerequisites for an understanding of the more advanced lectures of this volume. In particular the lectures by Prof. Landau are closely related.
The theory behind MC simulations is based on statistics and the analysis of MC generated data is applied statistics. Therefore, statistical concepts are reviewed first in this tutorial. Nowadays abundance of computational power implies also a paradigm shift with respect to statistics: Computationally intensive, but conceptually simple, methods belong at the forefront. MC simulations are not only relevant for simulating models of interest, but they constitute also a valuable tool for...
