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Functional regression via variational Bayes. (English) Zbl 1274.62200

Summary: 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.

MSC:

62F15 Bayesian inference
62G15 Nonparametric tolerance and confidence regions
62G09 Nonparametric statistical resampling methods
65C60 Computational problems in statistics (MSC2010)
62P10 Applications of statistics to biology and medical sciences; meta analysis
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References:

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