Partial Intrinsic Bayes Factor

• Activity Number: 448
• Type: Contributed
• Date/Time: Wednesday, August 10, 2005 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Yongsung Joo*+ and George Casella
• Companies: University of Florida and University of Florida
• Keywords: Bayes factor ; Bayesian model selection

Abstract

We often select a model from a finite number of candidate models, all of which encompass a small model. The idea of the Partial Intrinsic Bayes Factor ($BF^{p\_intrinsic}$) is to incorporate this information into a model selection criterion. Most the classical model selection criteria, such as $AIC$ and $BIC$, do not incorporate such knowledge into the selection procedure. Although the prior distribution in a Bayesian framework might be used to employ this information, there is not any clearly suggested objective rule to convert this information into a prior density. The $BF^{p\_intrinsic}$ divides the parameters into two groups. While the regular intrinsic Bayes factor ($BF^{intrinsic}$) starts with improper noninformative priors for every parameter, the $BF^{p\_intrinsic}$ uses proper informative priors with estimated hyper parameters using empirical Bayes for the parameters the analyst believes are important (i.e., constant, linear, and quadratic terms in photosynthetic rate example) and improper noninformative priors for the parameters of which importance he/she wants to verify (i.e., cubic and quartic terms in photosynthetic rate example).