Variance Reduction Using Nonreversible Langevin Samplers

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• 作者：A. B. Duncan ; T. Lelièvre ; G. A. Pavliotis
• 刊名：Journal of Statistical Physics
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：163
• 期：3
• 页码：457-491
• 全文大小：1,119 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Statistical Physics
  Mathematical and Computational Physics
  Physical Chemistry
  Quantum Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9613

文摘

A standard approach to computing expectations with respect to a given target measure is to introduce an overdamped Langevin equation which is reversible with respect to the target distribution, and to approximate the expectation by a time-averaging estimator. As has been noted in recent papers [30, 37, 61, 72], introducing an appropriately chosen nonreversible component to the dynamics is beneficial, both in terms of reducing the asymptotic variance and of speeding up convergence to the target distribution. In this paper we present a detailed study of the dependence of the asymptotic variance on the deviation from reversibility. Our theoretical findings are supported by numerical simulations.