Functional regression via variational bayes

Jeff Goldsmith, Matt P. Wand, Ciprian Crainiceanu

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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
StatePublished - 2011


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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