Mathematics Seminar Series: Probability

Title:    Stein Coupling.

Abstract:    Classically, Stein’s method transforms the problem of distributional approximation into the task of bounding the expectation of an associated operator. This perspective has led to a wide range of applications, particularly in models with complex dependence structures. Over time, several powerful sub-methods have emerged, including exchangeable pairs, dependency graphs, and size-biased couplings. In this talk, I will present the general framework of Stein couplings, introduced by Chen and Röllin, which unifies these approaches and extends the reach of Stein’s method to a broader class of models. If time permits, I will also discuss some of my favorite open problems that do not quite fit into the classical sub-method frameworks, but where Stein’s method still "should" apply.