title: Bayesian Case-deletion Model Complexity and Information Criterion.
abstract: We establish a connection between Bayesian case influence measures for assessing the influence of individual observations and Bayesian predictive methods for evaluating the predictive performance of a model and comparing different models fitted to the same dataset. Based on such a connection, we formally propose a new set of Bayesian case-deletion model complexity (BCMC) measures for quantifying the effective number of parameters in a given statistical model. Its properties in linear models are explored. Adding some functions of BCMC to a conditional deviance function leads to a Bayesian case-deletion information criterion (BCIC) for comparing models. We systematically investigate some properties of BCIC and its connection with other information criteria, such as the Deviance Information Criterion (DIC). We illustrate the proposed methodology on linear mixed models with simulations and a real data example.
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599, hzhu@bios.unc.edu.
authors.forename: Hongtu
authors.initials: H
authors.lastname: Zhu
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599, ibrahim@bios.unc.edu.
authors.forename: Joseph G
authors.initials: JG
authors.lastname: Ibrahim
authors.affiliation: Department of Biostatistics, Vanderbilt University, Nashville, TN, 37232, cindy.chen@vanderbilt.edu.
authors.forename: Qingxia
authors.initials: Q
authors.lastname: Chen
keywords: Bayesian; Case influence measures; Cross Validation; Information criterion; Markov chain Monte Carlo; Model complexity