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2017

Distance between configurations in Markov chain Monte Carlo simulations

Fukuma, Masafumi, Matsumoto, Nobuyuki, Umeda, Naoya

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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.

Distance between configurations in Markov chain Monte Carlo simulations · Around

Built on

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2013

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H. Fujii, D. Honda, M. Kato, Y. Kikukawa, S. Komatsu and T. Sano, “Hybrid Monte Carlo on Lefschetz thimbles - A study of the residual sign problem,” JHEP 1310

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M. Fukuma, N. Matsumoto and N. Umeda, work in progress

Cited in the paper.

J. Bloch, “Reweighting complex Langevin trajectories,” arXiv:1701.00986 [hep-lat]

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A. Alexandru, G. Başar, P. F. Bedaque and N. C. Warrington, “Tempered transitions between thimbles,” arXiv:1703.02414 [hep-lat]

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J. Nishimura and S. Shimasaki, “Combining the complex Langevin method and the generalized Lefschetz-thimble method,” arXiv:1703.09409 [hep-lat]

Cited in the paper.

Y. Mori, K. Kashiwa and A. Ohnishi, “Toward solving the sign problem with path optimization method,” arXiv:1705.05605 [hep-lat]

Original

Cited in the paper.

2016

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A. Alexandru, G. Başar, P. F. Bedaque, G. W. Ridgway and N. C. Warrington, “Sign problem and Monte Carlo calculations beyond Lefschetz thimbles,” JHEP 1605

2016

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M. Fukuma and N. Umeda, “Parallel tempering algorithm for integration over Lefschetz thimbles,” PTEP 2017

2017

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