Groupe d’études et de recherche en analyse des décisions

Bayesian Wavelet-Based Mixed Models for Functional Data

Jeffrey Morris

Many studies yield functional data, with the ideal units of observation curves and observed data sampled on a fine grid. These curves frequently have irregular features requiring spatially adaptive nonparametric representations. We discuss new methods for modeling these data using functional mixed models, which treat the curves as responses and relate them to covariates using nonparametric fixed and random effect functions. This Bayesian wavelet-based approach yields adaptively regularized posterior samples for all model parameters that can be used for any desired Bayesian estimation, inference or prediction. We illustrate this method on 4 applications yielding spiky functional data, and describe how it can be extended to deal with incomplete functional data for which some regions of some of the functions are missing, and to model higher dimensional functional data, e.g. images.