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March 2010 Bayesian functional {ANOVA} modeling using Gaussian process prior distributions
Cari G. Kaufman, Stephan R. Sain
Bayesian Anal. 5(1): 123-149 (March 2010). DOI: 10.1214/10-BA505


Functional analysis of variance (ANOVA) models partition a functional response according to the main effects and interactions of various factors. This article develops a general framework for functional ANOVA modeling from a Bayesian viewpoint, assigning Gaussian process prior distributions to each batch of functional effects. We discuss the choices to be made in specifying such a model, advocating the treatment of levels within a given factor as dependent but exchangeable quantities, and we suggest weakly informative prior distributions for higher level parameters that may be appropriate in many situations. We discuss computationally efficient strategies for posterior sampling using Markov Chain Monte Carlo algorithms, and we emphasize useful graphical summaries based on the posterior distribution of model-based analogues of traditional ANOVA decompositions of variance. We illustrate this process of model specification, posterior sampling, and graphical posterior summaries in two examples. The first considers the effect of geographic region on the temperature profiles at weather stations in Canada. The second example examines sources of variability in the output of regional climate models from a designed experiment.


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Cari G. Kaufman. Stephan R. Sain. "Bayesian functional {ANOVA} modeling using Gaussian process prior distributions." Bayesian Anal. 5 (1) 123 - 149, March 2010.


Published: March 2010
First available in Project Euclid: 22 June 2012

zbMATH: 1330.62341
MathSciNet: MR2596438
Digital Object Identifier: 10.1214/10-BA505

Keywords: Analysis of variance , Climate Models , functional data , variance components

Rights: Copyright © 2010 International Society for Bayesian Analysis


Vol.5 • No. 1 • March 2010
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