The Many Facets of Monte Carlo Methods: From Sampling Algorithms to Unbiased Estimators

Monte Carlo methods span a range of disciplines, drawing interest from statisticians, computer scientists, physicists, among others. In the Monte Carlo workflow, the upstream task involves designing and analyzing sampling algorithms, while the downstream task focuses on efficiently using these samples to form estimators. In this talk, I will discuss recent developments of both aspects. The first part introduces the 'Spectral Telescope' framework for analyzing Gibbs samplers, and discusses its relationship with the spectral independence technique recently developed in theoretical computer science. The second part focuses on the development of unbiased estimators through the combination of Markov Chain Monte Carlo and Multilevel Monte Carlo methods, highlighting their potential in parallel computing.

Biosketch: Guanyang Wang is an Assistant Professor in the Department of Statistics at Rutgers University. He completed his Ph.D. in Mathematics with a Ph.D. minor in Statistics at Stanford University, advised by Professor Persi Diaconis. Guanyang Wang's research primarily centers on Monte Carlo methods, applied probability, and statistical computing. Recently, he is also working on quantum computing. His research receives support from both the NSF and an Adobe Data Science Research Award.