Control functionals for Monte Carlo integration. (23rd May 2016)

• Record Type: Journal Article
• Authors: Oates, Chris J.; Girolami, Mark; Chopin, Nicolas
• Is Part Of: Journal of the Royal Statistical Society. Volume 79:Number 3(2017)
• Page Start: 695
• Page End: 718
• Publication Date: 2016-05-23
• Subjects: Control variates -- Non‐parametrics -- Reproducing kernel -- Stein's identity -- Variance reduction; Statistics -- Periodicals; Great Britain -- Statistics -- Periodicals; 519.2
• DOI: 10.1111/rssb.12185
• Languages: English
• ISSNs: 1369-7412

Abstract

Summary: 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.