JSM 2005 - Toronto

Abstract #302403

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 40
Type: Invited
Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
Sponsor: ENAR
Abstract - #302403
Title: Wavelet-based Functional Mixed Models
Author(s): Jeffrey S. Morris*+
Companies: The University of Texas M. D. Anderson Cancer Center
Address: 1515 Holcombe Blvd Box 447, Houston, TX, 77030-4009,
Keywords: Functional Data Analysis ; Nonparametric Regression ; Bayesian Methods ; Mixed Models ; Wavelets ; Proteomics
Abstract:

An increasing number of scientific studies yield functional data, in which the ideal observational units are curves and the observed data consist of curves sampled on a fine grid. In this paper, we present 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, with the full range of fixed effects and between-curve covariance structures available in mixed models. It yields nonparametric estimates of the fixed and random effects functions adaptively regularized using a nonlinear shrinkage prior on the fixed effects wavelet coefficients. Also yielded are estimates of the between-curve covariance matrices and within-curve covariance surfaces. The model is fit using MCMC, yielding posterior samples for all model quantities that can be used to perform Bayesian inference and prediction. This method is appropriate for spatially heterogeneous functional data, since its adaptive regularization procedure regularizes the functions with minimal attenuation of dominant local features. We illustrate the methodology on a cancer study involving mass spectrometry proteomics.

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Revised March 2005