Unbiased Estimators from Biased Algorithms

In many Monte Carlo settings, one wishes to compute the expectation of a stochastic object that can only be approximated. In such settings, the natural Monte Carlo estimator will be biased. In work of McLeish and Rhee/Glynn, it was shown how one can often construct unbiased estimators for such expectations. The idea turns out to be closely related to the multi-level Monte Carlo methods introduced by Giles. In this talk, we will survey some of the applications of this idea, and discuss some of the related theory for such algorithms. The ideas sometimes allow one to improve the rate of convergence for a given estimation problem from sub-canonical rate to “square root rate”. This work is joint with Jose Blanchet, Chang-Han Rhee, Guanyang Wang, Zeyu Zheng, and Zhengqing Zhou.

Bio: Professor Peter Glynn is a Thomas W. Ford Professor in the School of Engineering, Professor in the Department of Management Science and Engineering and the Institute for Computational and Mathematical Engineering, and Professor (by courtesy) in the Department of Electrical Engineering, all at Stanford University.

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