Hierarchical Bayesian Quantile Regression Model And Variable Selection Based On Mixed Truncated Normal Distribution

High-dimensional data is widely used in various fields of People's Daily life,such as social economy,biomedical science,signal processing and so on.High-dimensional data is usually characterized by strong correlation,high data dimension and sharp peak and thick tail distribution.Modeling and analysis of high-dimensional data is also a hot and frontier problem in modern statistical research.With the increase of variables of interest,it is a variable selection problem in statistics to select the variables that have a significant influence on the response variables and have a strong explanatory power,so as to improve the fitting accuracy of the joint model.In this thesis,we study the variable selection problem of hierarchical Bayesian quantile regression model under the condition of mixed truncated normal distribution,and compare and analyze the excellent effect of this variable selection method through simulation calculation.In this thesis,refer to the variable selection of existing models,and based on the expression form of mixed truncated normal distribution of asymmetric Laplace distribution,Lasso,Adaptive Lasso,Elastic Net and Adaptive Elastic Net quantile regression models are proposed.In this paper,the posterior distribution of model parameters is obtained by using the method of Bayesian analysis and Gibbs sampling,and the significant influencing variables of the response are screened out.Through numerical simulation and real data analysis,this thesis compares the advantages and disadvantages of variable screening among different models.The results show that this Bayesian Adaptive Elastic Net quantile regression model based on mixed truncated normal distribution performs best when applied to variable selection in the presence of a large number of predictors,collinearity and heterogeneity.