Bayesian Analysis

Bayes Factors for Smoothing Spline ANOVA

Chin-I. Cheng and Paul L. Speckman

Full-text: Open access

Abstract

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.

Article information

Source
Bayesian Anal., Volume 11, Number 4 (2016), 957-975.

Dates
First available in Project Euclid: 12 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.ba/1444653650

Digital Object Identifier
doi:10.1214/15-BA974

Mathematical Reviews number (MathSciNet)
MR3545470

Zentralblatt MATH identifier
1357.62254

Keywords
smoothing spline ANOVA Bayes factor laplace integration reproducing kernel semiparametric model

Citation

Cheng, Chin-I.; Speckman, Paul L. Bayes Factors for Smoothing Spline ANOVA. Bayesian Anal. 11 (2016), no. 4, 957--975. doi:10.1214/15-BA974. https://projecteuclid.org/euclid.ba/1444653650


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