Past Event: Babuška Forum

Scalable methods for Bayesian inversion

Peng Chen, Research Associate, Oden Institute

Abstract

Bayes’ rule provides an optimal framework to update the probability distribution of parameters with observation data and parameter-to-observable map. The central tasks of Bayesian inversion are to sample from the posterior distribution and compute statistics of some quantities of interest. However, critical challenges are faced when the parameter dimension is high and the parameter-to-observable map is expensive to evaluate, e.g., involving large-scale PDE solve. In this talk, I will introduce recent advances on computational methods to tackle these challenges by exploiting the geometry, smoothness, sparsity, intrinsic low-dimensionality, and low-rank properties of the posterior, which are shown to be scalable with respect to the parameter dimension and the complexity of the map approximation.