The Department of Mathematical Sciences will host Dr. Guanyang Wang, Assistant Professor of Statistics at Rutgers University–New Brunswick, for its math seminar series. Dr. Wang will present, “Unbiased Multilevel Monte Carlo methods for intractable distributions: MLMC meets MCMC.” This free seminar will take place on Friday, February 11, at 11 a.m. in BSB 132. A virtual option is also available: https://tinyurl.com/9nrnveur.
Constructing unbiased estimators from MCMC outputs has recently increased much attention in statistics and machine learning communities. However, the existing unbiased MCMC framework only works when the quantity of interest is an expectation of certain probability distribution. In this work, we propose unbiased estimators for functions of expectations. Our idea is based on the combination of the unbiased MCMC and MLMC methods. We prove our estimator has a finite variance, a finite computational complexity, and achieves ε-accuracy with O(1/ε²) computational cost under mild conditions. We also illustrate our estimator on several numerical examples. This is a joint work with Tianze Wang.