Fast Joint Functional Regression Modeling via Variational Bayes

• Activity Number: 219
• Type: Invited
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Jeff Goldsmith*+ and Matt Wand and Ciprian Crainiceanu
• Companies: The Johns Hopkins University and University of Technology and The Johns Hopkins University
• Keywords: Approximate Bayesian inference ; Markov chain Monte Carlo ; penalized splines

Abstract

We introduce variational Bayes methods for fast approximate inference in functional regression analysis. Both the standard cross-sectional and the increasingly common longitudinal settings are treated. The methodology allows Bayesian functional regression analyses to be conducted without the computational overhead of Monte Carlo methods. Confidence intervals of the model parameters are obtained both using the approximate variational approach and nonparametric resampling of clusters. The latter approach is possible because our variational Bayes functional regression approach is computationally efficient. A simulation study indicates that variational Bayes is highly accurate in estimating the parameters of interest and in approximating the Markov chain Monte Carlo-sampled joint posterior distribution of the model parameters. The methods apply generally, but are motivated by a longitudinal neuroimaging study of multiple sclerosis patients. Code used in simulations is made available as a web-supplement.