Warp Bridge Sampling: The Next Generation
Warp Bridge Sampling: The Next Generation
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DOI：
10.1080/01621459.2020.1825447
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发表时间：
2016-09
影响因子：
3.7
通讯作者：
Lazhi Wang;David E. Jones;X. Meng
中科院分区：
文献类型：
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作者：
Lazhi Wang;David E. Jones;X. Meng
抽象的桥采样是一种有效的蒙特卡洛（MC）方法，用于估计两个概率密度的归一化常量，这是统计，物理，化学和其他领域的常规计算问题。在单峰密度的情况下，这两个密度之间的重叠量，扭曲，II和III转换有效地增加了初始重叠，但对于多模式密度而言，它们较少。旨在将多模式的密度转换为单峰的（因此“ U”），而无需更改其归一化常数。归一化常量是未知的，然后将其映射到其生成分布的情况下，将其用于p，我们通常表示的翘曲版本。并且，就任何F差异而言，我们都不小于P和P之间的重叠并与相同的数据拟合。方法是在线提供的补充材料。
Abstract Bridge sampling is an effective Monte Carlo (MC) method for estimating the ratio of normalizing constants of two probability densities, a routine computational problem in statistics, physics, chemistry, and other fields. The MC error of the bridge sampling estimator is determined by the amount of overlap between the two densities. In the case of unimodal densities, Warp-I, II, and III transformations are effective for increasing the initial overlap, but they are less so for multimodal densities. This article introduces Warp-U transformations that aim to transform multimodal densities into unimodal ones (hence “U”) without altering their normalizing constants. The construction of a Warp-U transformation starts with a normal (or other convenient) mixture distribution that has reasonable overlap with the target density p, whose normalizing constant is unknown. The stochastic transformation that maps back to its generating distribution is then applied to p yielding its Warp-U version, which we denote . Typically, is unimodal and has substantially increased overlap with . Furthermore, we prove that the overlap between and is guaranteed to be no less than the overlap between p and , in terms of any f-divergence. We propose a computationally efficient method to find an appropriate , and a simple but effective approach to remove the bias which results from estimating the normalizing constant and fitting with the same data. We illustrate our findings using 10 and 50 dimensional highly irregular multimodal densities, and demonstrate how Warp-U sampling can be used to improve the final estimation step of the Generalized Wang–Landau algorithm, a powerful sampling and estimation approach. Supplementary materials for this article are available online.