Bayes factors for smoothing spline ANOVA

Chin I. Cheng, Paul L. Speckman

Research output: Contribution to journalArticlepeer-review


This paper describes an approach for variable selection and hypothesis testing in semiparametric additive models using Bayes factors in smoothing spline analysis of variance (SSANOVA) models. Effects can be linear or nonparametric (i.e., smooth or interactions between selected linear and smooth effects). To evaluate the importance of each term in the model, we develop Bayes factors for both linear and nonparametric terms. We compute approximate Bayes factors by Monte Carlo and Laplace integration. These Bayes factors can be computed to compare any two sub-models including one model nested in another. This permits formal tests of any portion or simultaneous portions of an SSANOVA model. We demonstrate this approach with an example.

Original languageEnglish
Pages (from-to)957-975
Number of pages19
JournalBayesian Analysis
Issue number4
StatePublished - Dec 1 2016


  • Bayes factor
  • Laplace integration
  • Reproducing kernel
  • Semiparametric model
  • Smoothing spline ANOVA


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