Bayesian Shrinkage Estimators of Quality Parameters in Ultrahigh-Dimensional Generalized Linear Models.

One of the basic issues in Ultrahigh-dimensional data analysis is fitting the optimal model and estimating its unknown quality parameters in such a way that it can correctly interpret the structure of the investigated data. In this article, we compare two non-local hyper priors: hyper product moment and hyper product inverse moment priors in determining the optimal model at the same time as estimating the parameters in variable selection using Bayesian Shrinkage in ultrahigh-dimensional generalized linear models. In order to compute the posterior probabilities, the Laplace approximation method was used, and to select the optimal model in the model space of posterior probabilities, Simplified shotgun stochastic search algorithm with screening (S5) for GLMs was used along with screening. Finally, through the study of simulation and real data analysis, the effectiveness of the above Bayesian Shrinkage methods has been evaluated with the ISIS-LASSO and ISIS-SCAD method. The advantage of the model is shown.