Convergence Rates for a Class of Estimators Based on Stein's Method

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Title: Convergence Rates for a Class of Estimators Based on Stein's Method
Authors: Oates, CJ
Cockayne, J
Briol, F-X
Girolami, M
Item Type: Journal Article
Abstract: Gradient information on the sampling distribution can be used to reduce the variance of Monte Carlo estimators via Stein's method. An important application is that of estimating an expectation of a test function along the sample path of a Markov chain, where gradient information enables convergence rate improvement at the cost of a linear system which must be solved. The contribution of this paper is to establish theoretical bounds on convergence rates for a class of estimators based on Stein's method. Our analysis accounts for (i) the degree of smoothness of the sampling distribution and test function, (ii) the dimension of the state space, and (iii) the case of non-independent samples arising from a Markov chain. These results provide insight into the rapid convergence of gradient-based estimators observed for low-dimensional problems, as well as clarifying a curse-of-dimension that appears inherent to such methods.
Issue Date: 1-May-2019
URI: http://hdl.handle.net/10044/1/53205
Copyright Statement: © The Authors
Keywords: math.ST
stat.TH
Notes: Major revision of the manuscript
Appears in Collections:Mathematics
Faculty of Natural Sciences



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