Using Perturbed Underdamped Langevin Dynamics to Efficiently Sample from Probability Distributions
Using Perturbed Underdamped Langevin Dynamics to Efficiently Sample from Probability Distributions
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DOI：
10.1007/s10955-017-1906-8
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发表时间：
2017-12-01
影响因子：
1.6
通讯作者：
Pavliotis, G. A.
中科院分区：
文献类型：
--
作者：
Duncan, A. B.;Nusken, N.;Pavliotis, G. A.
在本文中，我们介绍和分析朗之万采样器，包括扰动的标准欠阻尼朗之万动力学。扰动动力学是这样的，它的不变测度与未扰动动力学的不变测度相同。我们表明，适当的选择的扰动可以导致采样器，具有改善的性能，至少在减少渐近方差。我们提出了一个详细的分析，新的Langevin采样高斯目标分布。我们的理论结果支持与非高斯目标措施的数值实验。
In this paper we introduce and analyse Langevin samplers that consist of perturbations of the standard underdamped Langevin dynamics. The perturbed dynamics is such that its invariant measure is the same as that of the unperturbed dynamics. We show that appropriate choices of the perturbations can lead to samplers that have improved properties, at least in terms of reducing the asymptotic variance. We present a detailed analysis of the new Langevin sampler for Gaussian target distributions. Our theoretical results are supported by numerical experiments with non-Gaussian target measures.