Composite Likelihood Bayesian Information Criteria for Model Selection in High-Dimensional Data

For high-dimensional data sets with complicated dependency structures, the full likelihood approach often leads to intractable computational complexity. This imposes difficulty on model selection, given that most traditionally used information criteria require evaluation of the full likelihood. We propose a composite likelihood version of the Bayes information criterion (BIC) and establish its consistency property for the selection of the true underlying marginal model. Our proposed BIC is shown to be selection-consistent under some mild regularity conditions, where the number of potential model parameters is allowed to increase to infinity at a certain rate of the sample size. Simulation studies demonstrate the empirical performance of this new BIC, especially for the scenario where the number of parameters increases with sample size. Technical proofs of our theoretical results are provided in the online supplemental materials.