Functional regression via variational bayes

Jeff Goldsmith, Matt P. Wand, Ciprian M Crainiceanu

Research output: Contribution to journalArticle

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 method- ology allows Bayesian functional regression analyses to be conducted with- out the computational overhead of Monte Carlo methods. Confidence in- tervals 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 ap- proach is computationally efficient. A simulation study indicates that varia- tional 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.

Original languageEnglish (US)
Pages (from-to)572-602
Number of pages31
JournalElectronic Journal of Statistics
Volume5
DOIs
StatePublished - 2011

Fingerprint

Variational Bayes
Regression
Bayes Method
Multiple Sclerosis
Neuroimaging
Functional Analysis
Variational Approach
Bayes
Resampling
Markov Chain Monte Carlo
Posterior distribution
Regression Analysis
Joint Distribution
Variational Methods
Monte Carlo method
Confidence interval
Simulation Study
Model
Simulation

Keywords

  • Approximate bayesian inference
  • Markov chain monte carlo
  • Penalized splines

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Functional regression via variational bayes. / Goldsmith, Jeff; Wand, Matt P.; Crainiceanu, Ciprian M.

In: Electronic Journal of Statistics, Vol. 5, 2011, p. 572-602.

Research output: Contribution to journalArticle

Goldsmith, Jeff ; Wand, Matt P. ; Crainiceanu, Ciprian M. / Functional regression via variational bayes. In: Electronic Journal of Statistics. 2011 ; Vol. 5. pp. 572-602.
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