Mixtures of g-priors for analysis of variance models with a diverging number of parameters
Document Type
Article
Publication Date
6-1-2017
Abstract
© 2017 International Society for Bayesian Analysis. We consider Bayesian approaches for the hypothesis testing problem in the analysis-of-variance (ANOVA) models. With the aid of the singular value decomposition of the centered designed matrix, we reparameterize the ANOVA models with linear constraints for uniqueness into a standard linear regression model without any constraint. We derive the Bayes factors based on mixtures of g-priors and study their consistency properties with a growing number of parameters. It is shown that two commonly used hyper-priors on g (the Zellner-Siow prior and the beta-prime prior) yield inconsistent Bayes factors due to the presence of an inconsistency region around the null model. We propose a new class of hyper-priors to avoid this inconsistency problem. Simulation studies on the two-way ANOVA models are conducted to compare the performance of the proposed procedures with that of some existing ones in the literature.
Publication Title
Bayesian Analysis
Recommended Citation
Wang, M.
(2017).
Mixtures of g-priors for analysis of variance models with a diverging number of parameters.
Bayesian Analysis,
12(2), 511-532.
http://doi.org/10.1214/16-BA1011
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/13131