Transport methods for simulation-based Bayesian inference and data assimilation (Youssef Marzouk -- MIT)

Many practical Bayesian inference problems fall into the simulation-based or "likelihood-free" setting, where evaluations of the likelihood function or prior density are unavailable or intractable; instead one can only draw samples from the joint parameter-data prior. Learning conditional distributions is essential to the solution of these problems. To this end, I will discuss a powerful class of methods for conditional density estimation and conditional simulation based on transportation of measure. An important application for these methods lies in data assimilation for dynamical systems, where transport enables new approaches to nonlinear filtering and smoothing. I will also present related methods for joint dimension reduction of data and parameters in data assimilation and other non-Gaussian inference problems. Time permitting, I will also discuss some new results on the statistical convergence of transport-based density estimators. This is joint work with Ricardo Baptista, Max Ramgraber, Alessio Spantini, Sven Wang, and Olivier Zahm.