A0572
Title: A RKHS-based Bayesian approach to functional regression
Authors: Jose Berrendero - Universidad Autonoma de Madrid (Spain)
Antonio Coin - Universidad Autonoma de Madrid (Spain) [presenting]
Antonio Cuevas - Autonomous University of Madrid (Spain)
Abstract: A novel Bayesian methodology is proposed for inference in functional linear and logistic regression models based on the theory of reproducing kernel Hilbert spaces (RKHS's). General models are introduced that build upon the RKHS generated by the covariance function of the underlying stochastic process and whose formulation includes, in particular cases, all finite-dimensional models based on linear combinations of marginals of the process, which can collectively be seen as dense subspace made of simple approximations. By imposing a suitable prior distribution on this dense functional space, data-driven inference is performed via standard Bayes methodology, estimating the posterior distribution through reversible jump Markov chain Monte Carlo methods. In this context, the contribution is two-fold. First, a theoretical result is derived that guarantees posterior consistency based on an application of a classic theorem of Doob to the RKHS setting. Second, it is shown that several prediction strategies stemming from the Bayesian procedure are competitive against other usual alternatives in both simulations and real data sets, including a Bayesian-motivated variable selection method.
