23rd April 2020, 10am:

Neil Chada (National University of Singapore)

Title: Advancements of non-Gaussian random fields for statistical inversion

Abstract: Developing informative priors for Bayesian inverse problems is an important direction, which can help quantify information on the posterior. In this talk we introduce a new of a class priors for inversion based on $\alpha$-stable sheets, which incorporate multiple known processes such as a Gaussian and Cauchy process. We analyze various convergence properties which is achieved through different representations these sheets can take. Other aspects we wish to address are well-posedness of the inverse problem and finite-dimensional approximations. To complement the analysis we provide some connections with machine learning, which will allow us to use sampling based MCMC schemes. We will conclude the talk with some numerical experiments, highlighting the robustness of the established connection, on various inverse problems arising in regression and PDEs.