Grad Student Seminar: Michael Conroy
Efficient rare-event simulation for branching processes
In this talk I’ll discuss some of my past, current, and future work with importance sampling schemes for maxima of branching processes. In a recent paper, my collaborators and I developed a strongly efficient and unbiased estimator for tail events of the maximum of a branching random walk with perturbation (or a Galton-Watson process on a random tree). The sampling procedure relies on a change of measure applied to the entire tree that randomly selects one branch to which it applies an exponential tilt, leaving other branches unchanged. The process of selecting a single path suggests that alterations can be made to the estimator to reduce the computational complexity associated with a large branching rate. It also allows us to conjecture a conditional limit theorem that provides insight into how extreme events occur in branching random walks. I plan to make this talk very accessible, starting with the basics of importance sampling and exponential tilting. This talk includes joint work with Mariana Olvera-Cravioto, Bojan Basrak (University of Zagreb), and Zbigniew Palmowski (Wroclaw University of Science and Technology).