Bayesian Inference Using Hyper Product Inverse Moment Prior in the Ultrahigh-Dimensional Generalized Linear Models

In this paper, we considered a Bayesian hierarchical method using the hyper product inverse momentprior in the ultrahigh-dimensional generalized linear model (UDGLM), that was useful in the Bayesianvariable selection. We showed the posterior probabilities of the true model converge to 1 as the samplesize increases. For computing the posterior probabilities, we implemented the Laplace approximation.The Simplified Shotgun Stochastic Search with Screening (S5) procedure for generalized linear modelwas suggested for exploring the posterior space. Simulation studies and real data analysis using theBayesian ultrahigh-dimensional generalized linear model indicate that the proposed method had better performance than the previous models.