A New Bayesian information criterion for high dimensional analysis

The significance of information criteria in model selection cannot be overstated, particularly within high-dimensional contexts. Various approaches have been developed to address this challenge, such as the High Dimensional Bayesian Information Criteria (HBIC) and the Extended Bayesian Information Criterion (EBIC), which have demonstrated utility in both theoretical frameworks and practical applications. Nevertheless, the delicate equilibrium between unknown parameters and model complexity warrants further investigation. In this study, we introduce a novel Bayesian information criterion capable of accommodating rapid covariate dimensionality expansion relative to sample size. We establish model selection consistency for both unpenalized and penalized estimators. Through extensive simulation analyses across commonly encountered models, our proposed criterion, termed Improved Bayesian Information Criterion (IBIC), exhibits significant enhancements over established competitors. Two gene associated real data analysis also demonstrate encouraging results. Furthermore, we show that IBIC can be applied to the generalized linear model in the same way as linear models.