Beskos, A; Pillai, NS; Roberts, GO; Sanz-Serna, JM; Stuart, AM; (2010) The Acceptance Probability of the Hybrid Monte Carlo Method in High-Dimensional Problems. In: Simos, TE and Psihoyios, G and Tsitouras, C, (eds.) **NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS I-III.** (pp. 23 - 26). AMER INST PHYSICS

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## Abstract

We investigate the properties of the Hybrid Monte-Carlo algorithm in high dimensions. In the simplified scenario of independent, identically distributed components, we prove that, to obtain an 0(1) acceptance probability as the dimension d of the state space tends to infinity, the Verlet/leap-frog step-size h should be scaled as h = l x d(-1/4). We also identify analytically the asymptotically optimal acceptance probability, which turns out to be 0.651 (with three decimal places); this is the choice that optimally balances the cost of generating a proposal, which decreases as l increases, against the cost related to the average number of proposals required to obtain acceptance, which increases as increases.

Type: | Proceedings paper |
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Title: | The Acceptance Probability of the Hybrid Monte Carlo Method in High-Dimensional Problems |

Event: | International Conference on Numerical Analysis and Applied Mathematics |

Location: | Rhodes, GREECE |

Dates: | 2010-09-19 - 2010-09-25 |

ISBN-13: | 978-0-7354-0834-0 |

Keywords: | Hybrid Monte Carlo, Hamiltonian dynamics, Verlet method, Geometric integration |

UCL classification: | UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science |

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