Title: Posterior contraction rates for Bayesian functional linear regression
Authors: Giuseppe Di Benedetto - University of Oxford (United Kingdom) [presenting]
Judith Rousseau - University of Oxford (United Kingdom)
Abstract: Functional linear regression (FLR) has been thoroughly studied in the frequentist literature. We consider a Bayesian approach to FLR with scalar response and random functional covariate. Using a sieve prior for the slope parameter, we investigate the asymptotic properties of its posterior distribution. The model can be studied as an ill-posed inverse problem and we provide contraction rates for the direct and inverse problems, namely the posterior contraction rates with respect to the prediction risk and the $L_2$ norm.