Distance between configurations in Markov chain Monte Carlo simulations

• Fukuma, Masafumi

  Department of Physics, Kyoto University

• Matsumoto, Nobuyuki

  Department of Physics, Kyoto University

• Umeda, Naoya

  Department of Physics, Kyoto University

Abstract

For a given Markov chain Monte Carlo algorithm we introduce a distance between two configurations that quantifies the difficulty of transition from one configuration to the other configuration. We argue that the distance takes a universal form for the class of algorithms which generate local moves in the configuration space. We explicitly calculate the distance for the Langevin algorithm, and show that it certainly has desired and expected properties as distance. We further show that the distance for a multimodal distribution gets dramatically reduced from a large value by the introduction of a tempering method. We also argue that, when the original distribution is highly multimodal with large number of degenerate vacua, an anti-de Sitter-like geometry naturally emerges in the extended configuration space.

Journal

• Journal of High Energy Physics

  Journal of High Energy Physics 2017 (12), 001-, 2017-12-01

  Springer Berlin Heidelberg

Keywords

• Random Systems
• Stochastic Processes
• Lattice QCD
• AdS-CFT Correspondence

Details

• CRID: 1050564285808215936
• NII Article ID: 120006410715
• ISSN: 11266708
• ISSN: 10298479
• DOI: 10.1007/jhep12(2017)001
• HANDLE: 2433/229549
• Web Site: http://link.springer.com/content/pdf/10.1007/JHEP12(2017)001.pdf
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN