Importance Sampling: Intrinsic Dimension and Computational Cost
Importance Sampling: Intrinsic Dimension and Computational Cost
复制标题
DOI：
10.1214/17-sts611
复制
发表时间：
2017-08-01
影响因子：
5.7
通讯作者：
Stuart, A. M.
中科院分区：
文献类型：
--
作者：
Agapiou, S.;Papaspiliopoulos, O.;Stuart, A. M.
重要性抽样的基本思想是使用来自建议度量的独立样本，以便近似于目标度量的期望。为了保证精确的近似，了解需要多少样本是关键。直观地说，目标和提案之间的距离概念应该决定该方法的计算成本。一个主要的挑战是根据与从业者相关的参数或统计数据来量化这个距离。这个主题已经引起了各个社区的极大兴趣。本文的目的是通过创建一个总体框架来概述和统一由此产生的文献。给出了一个一般理论，重点讨论了重要性抽样在贝叶斯反问题和滤波中的应用。
The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee accurate approximations. Intuitively, some notion of distance between the target and the proposal should determine the computational cost of the method. A major challenge is to quantify this distance in terms of parameters or statistics that are pertinent for the practitioner. The subject has attracted substantial interest from within a variety of communities. The objective of this paper is to overview and unify the resulting literature by creating an overarching framework. A general theory is presented, with a focus on the use of importance sampling in Bayesian inverse problems and filtering.