Infinite-dimensional Stein’s method with applications
Stein’s method is a powerful tool for bounding distances between probability distributions. Originally used to study the rate of distributional convergence in various limit theorems, it has recently seen numerous applications to computational statistics and machine learning. Among those is measuring the sample quality in approximate MCMC and building goodness-of-fit tests. I will speak about my work in the area of Stein’s method for infinite-dimensional probability laws and its applications to functional limit theorems. I will also briefly describe some of the results I have obtained together with Jonathan Huggins, Trevor Campbell and Tamara Broderick related to bounding the error of posterior mean and uncertainty estimates arising in approximate Bayesian inference. Finally, I will talk about what I think is an interesting direction for future research, which is related to studying approximate Gaussian Process inference using Stein’s method and building a Stein-based GP goodness-of-fit test.