ربابه حسین پورصمیم ممقانی

One of the basic problems in Ultrahigh-dimensional data analysis is fitting the optimal model and estimating its unknown parameters in such a way that it can correctly interpret the struc[۱]ture of the investigated data. In applied statistics, the use of penalized likelihood methods in optimal model selection and estimating the effects of important variables in high-dimensional situations are very common, but in terms of computation, they create a lot of time and cost to inferencing models. Recent studies show that when the sample size is large, most of the Bayesian methods are more efficient than the penalized likelihood methods in predicting the model. In this thesis, in order to reduce the overfitting caused by the ultrahigh-dimensional variables, in Bayesian shirinkage variable selection methods for generalized linear models, we use two nonlocal hyper priors: product moment and product inverse moment. We determine the optimal model at the same time as estimating the parameters of the model and studying the optimal properties of the posterior probability with the product inverse moment prior. In order to calculate the posterior probabilities, the Laplace approximation method is used, and for the optimal model selection in the condensed space of posterior probabilities, the simplified shotgun stochastic search algorithm with screening (S۵) for GLMs is applied. Fi[۱]nally, through the simulation study and real data analysis related to leukemia disease and data related to checking the efficiency of engines produced by Bronze Industrial Group, which manufactures car engines, the efficiency of the proposed Bayesian shirinkage methods and the ISIS-LASSO and ISIS-SCAD penalized likelihood methods have been evaluated.

Keywords: ISIS-LASSO, ISIS-SCAD, Nonlocal Prior, Penalized likelihood, Sure Indepen[۱]dence Screening, Ultrahigh Dimensional, Variable