Bayesian density regression with functional covariates - modelling and visualisation
This thesis develops models, techniques, and visualization tools for nonparametric Bayesian regression with a scalar response and a functional covariate (possibly subject to measurement error). In particular, one of the contributions of this thesis consists of an infinite mixture of functional linear models, which we show to be tantamount to a dependent Dirichlet process, and that can be employed on a scalar-on-function regression framework. Another contribution of this thesis rests on the development of a suite of visualization tools within the proposed regression framework—including what we will refer to as the GYM plot—for examining the effect of a functional covariate on a scalar output. Finally, we devise versions of the so-called simulation-extrapolation algorithm (SIMEX) adapted to our functional regression framework of interest to handle measurement error in the proposed infinite mixture of functional linear models. A battery of numerical experiments and Monte Carlo simulations are conducted, overall suggesting a good performance of the proposed framework. Finally, we showcase the application of the proposed methods in a case study in finance which reveals interesting links between economic growth and yield curves.