Electronic Journal of Statistics

Functional regression via variational Bayes

Jeff Goldsmith, Matt P. Wand, and Ciprian Crainiceanu

Full-text: Open access

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.

Article information

Source
Electron. J. Statist. Volume 5 (2011), 572-602.

Dates
First available in Project Euclid: 15 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1308143123

Digital Object Identifier
doi:10.1214/11-EJS619

Mathematical Reviews number (MathSciNet)
MR2813555

Zentralblatt MATH identifier
1274.62200

Keywords
Approximate Bayesian inference Markov chain Monte Carlo penalized splines

Citation

Goldsmith, Jeff; Wand, Matt P.; Crainiceanu, Ciprian. Functional regression via variational Bayes. Electron. J. Statist. 5 (2011), 572--602. doi:10.1214/11-EJS619. https://projecteuclid.org/euclid.ejs/1308143123


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