Bayesian functional ANOVA modeling using Gaussian process prior distributions
By Cari Kaufman, Stephan R. Sain. 2010
150 citations recorded by the source corpus.
Functional analysis of variance (ANOVA) models partition a func- tional response according to the main efiects 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 efiects. 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 e-cient 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 decom- positions of variance. We illustrate this process of model speciflcation, posterior sampling, and graphical posterior summaries in two examples. The flrst consid- ers the efiect of geographic region on the temperature proflles at weather stations in Canada. The second example examines sources of variability in the output of regional climate models from a designed experiment.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/05186498a81c026e6112f3b38cebcac2b1a6a211
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In Artificial Intelligence
- David Kristjanson Duvenaud
- Hannes Nickisch
- Carl E. Rasmussen
- Eric-Jan Wagenmakers
- Ruud Wetzels
- Andrew Gordon Wilson
- Raoul P. P. P. Grasman
- Sergey Levine
In Statistics and Probability
- Eric-Jan Wagenmakers
- Ruud Wetzels
- David Kristjanson Duvenaud
- Hannes Nickisch
- Raoul P. P. P. Grasman
- Carl E. Rasmussen
- John K. Kruschke
- Zoltan Dienes
Citations in the corpus
- A Default Bayesian Hypothesis Test for ANOVA Designs (2012, background): “, Draper and Smith 1998; Faraway 2002) and, although the Bayesian treatment of ANOVA is gaining popularity (e.g., Gelman et al. 2004; Qian and Shen 2007; Ntzoufras 2009; Kaufman and Sain 2010), the latter has dealt almost exclusively with estimation, not testing (for exceptions, see Westfall and Gön”
- Additive Gaussian Processes (2011, methodology): “A related functional ANOVA GP model [9] decomposes the mean function into a weighted sum of GPs.”