Wavelet-based Functional Mixed Models

• Activity Number: 386
• Type: Contributed
• Date/Time: Wednesday, August 11, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jeffrey S. Morris*+
• Companies: University of Texas M.D. Anderson Cancer Center
• Keywords: functional data analysis ; wavelets ; Bayesian methods ; shrinkage estimators ; mixed models

Abstract

An ever-increasing number of studies yield functional data, where the ideal observational units are curves and the observed data consist of sets of curves sampled on a fine grid. We develop new methodology generalizing the linear mixed model to the functional mixed model framework, with model-fitting done using a Bayesian wavelet-based approach. This method is very flexible, accommodating functions of arbitrary form and the full range of fixed effects between-curve covariance structures of the mixed models framework. It yields nonparametric estimates of the fixed and random effects functions that are adaptively regularized via a nonlinear shrinkage prior on the fixed effects' wavelet coefficients, plus estimates of any between-curve and within-curve correlation surfaces. Posterior samples allow us to perform Bayesian inference on all model quantities. This method is appropriate for functional data characterized by numerous local features like peaks, since our adaptive regularization procedure regularizes the functions with minimal attenuation of dominant local features. We apply this method to complex and irregular functional data from two biological studies.