Estimating errors reliably in Monte Carlo simulations of the Ehrenfest model

被引：36

作者：

Ambegaokar, Vinay ^{[1
]}

Troyer, Matthias ^{[2
]}

机构：

[1] Cornell Univ, Atom & Solid State Phys Lab, Ithaca, NY 14853 USA

[2] ETH, Theoret Phys, CH-8093 Zurich, Switzerland

来源：

AMERICAN JOURNAL OF PHYSICS | 2010年 / 78卷 / 02期

关键词：

Markov processes; Monte Carlo methods; physics education;

D O I：

10.1119/1.3247985

中图分类号：

G40 [教育学];

学科分类号：

040101 ; 120403 ;

摘要：

We use the Ehrenfest urn model to illustrate the subtleties of error estimation in Monte Carlo simulations. We discuss how the smooth results of correlated sampling in Markov chains can fool one's perception of the accuracy of the data and show via numerical and analytical methods how to obtain reliable error estimates from correlated samples.

引用

页码：150 / 157

页数：8

共 14 条

[1] The ALPS project release 1.3:: Open-source software for strongly correlated systems [J].

Albuquerque, A. F. ;

Alet, F. ;

Corboz, P. ;

Dayal, P. ;

Feiguin, A. ;

Fuchs, S. ;

Gamper, L. ;

Gull, E. ;

Guertler, S. ;

Honecker, A. ;

Igarashi, R. ;

Koerner, M. ;

Kozhevnikov, A. ;

Laeuchli, A. ;

Manmana, S. R. ;

Matsumoto, M. ;

McCulloch, I. P. ;

Michel, F. ;

Noack, R. M. ;

Pawlowski, G. ;

Pollet, L. ;

Pruschke, T. ;

Schollwoeck, U. ;

Todo, S. ;

Trebst, S. ;

Troyer, M. ;

Werner, P. ;

Wessel, S. .

JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS, 2007, 310 (02) :1187-1193

[2] The ALPS Project: Open Source Software for Strongly Correlated Systems [J].

Alet, F. ;

Dayal, P. ;

Grzesik, A. ;

Honecker, A. ;

Koerner, M. ;

Laeuchli, A. ;

Manmana, S. R. ;

McCulloch, I. P. ;

Michel, F. ;

Noack, R. M. ;

Schmid, G. ;

Schollwoeck, U. ;

Stoeckli, F. ;

Todo, S. ;

Trebst, S. ;

Troyer, M. ;

Werner, P. ;

Wessel, S. .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2005, 74 :30-35

[3] Entropy and time [J].

Ambegaokar, V ;

Clerk, AA .

AMERICAN JOURNAL OF PHYSICS, 1999, 67 (12) :1068-1073

[4]

AMBEGAOKAR V, 1996, REASONING LUCK PROBA, P174

[5]

[Anonymous], 1947, AM MATH MON, DOI DOI 10.2307/2304386

[6]

ECKHARDT R, 1987, LOS ALAMOS SCI, V15, P125

[7]

Ehrenfest PUT, 1907, PHYS Z, V8, P311

[8]

EMCH G, 2000, LOGIC THERMOSTATIC P, P106

[9]

GOULD H, 2007, INTRO COMPUTER SIMUL, P427

[10]

Krauth W., 2006, STAT MECH ALGORITHMS

← 1 2 →