Gaussian Process Models for Non Parametric Functional Regression with Functional Responses

Nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a Gaussian process model whose posterior mode coincide with the fRKHS estimator. The Bayesian approach has several advantages compared to its predecessor. We also use the predictive process models adapted from the spatial statistics literature to overcome the computational limitations. Modifications of predictive process models are nevertheless critical in our context to obtain valid inferences. The numerical results presented demonstrate the effectiveness of the modifications.