Bayesian density regression with functional covariates - modelling and visualisation
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Date
24/05/2023Author
Bernieri, Emmanuel
Metadata
Abstract
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.