Control functionals for Monte Carlo integration

• 成果类型: Article
• 署名作者: Oates, Chris J.; Girolami, Mark; Chopin, Nicolas
• 署名单位: University of Technology Sydney; University of Warwick; Alan Turing Institute; Institut Polytechnique de Paris; ENSAE Paris; Institut Polytechnique de Paris; ENSAE Paris
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12185
• 发表日期: 2017
• 页码: 695-718
• 关键词: principle; models

摘要

A non-parametric extension of control variates is presented. These leverage gradient information on the sampling density to achieve substantial variance reduction. It is not required that the sampling density be normalized. The novel contribution of this work is based on two important insights: a trade-off between random sampling and deterministic approximation and a new gradient-based function space derived from Stein's identity. Unlike classical control variates, our estimators improve rates of convergence, often requiring orders of magnitude fewer simulations to achieve a fixed level of precision. Theoretical and empirical results are presented, the latter focusing on integration problems arising in hierarchical models and models based on non-linear ordinary differential equations.