Concepts in Monte Carlo sampling

IF 0.8 4区教育学 Q3 EDUCATION, SCIENTIFIC DISCIPLINES

American Journal of Physics Pub Date : 2023-09-06 DOI:10.1119/5.0176853

Gabriele Tartero, Werner Krauth

引用次数: 0

Abstract

We discuss contemporary ideas in Monte Carlo algorithms in the simplified setting of the one-dimensional anharmonic oscillator. After reviewing the connection between molecular dynamics and Monte Carlo, we introduce the Metropolis and the factorized Metropolis algorithms and lifted non-reversible Markov chains. We, furthermore, illustrate the concept of thinning, where moves are accepted by simple bounding potentials rather than the harmonic and quartic contributions to the anharmonic oscillator. We point out the multiple connections of our example algorithms with real-world sampling problems. This paper is self-contained, and Python implementations are provided.

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蒙特卡罗抽样的概念

我们以简化的一维非谐振子为背景，讨论蒙特卡罗算法的当代思想。在回顾了分子动力学与蒙特卡洛之间的联系之后，我们介绍了 Metropolis 算法和因子化 Metropolis 算法，以及提升的非可逆马尔可夫链。此外，我们还说明了 "稀化"（thinning）的概念，即通过简单的边界势（bounding potentials）而不是谐波和四次谐波对非谐振荡器的贡献来接受移动。我们指出了我们的示例算法与现实世界采样问题的多种联系。本文自成一体，并提供了 Python 实现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

American Journal of Physics 物理-物理：综合

CiteScore

1.80

自引率

11.10%

发文量

146

审稿时长

3 months

期刊介绍： The mission of the American Journal of Physics (AJP) is to publish articles on the educational and cultural aspects of physics that are useful, interesting, and accessible to a diverse audience of physics students, educators, and researchers. Our audience generally reads outside their specialties to broaden their understanding of physics and to expand and enhance their pedagogical toolkits at the undergraduate and graduate levels.