Bayesian Variable Selection Of Regression Model With Dependent Errors

In recent years,statistical research based on regression models has attracted more and more attention from scholars.In the rapid development of contemporary society,high-dimensional data can be seen everywhere,but not all data is meaningful.In order to reduce costs and reduce consumption,people are more concerned about some important variables.Therefore,the variable choice for high-dimensional data is An important research topic.Bayesian method stands out among many variable selection methods with its efficient estimation efficiency and flexible mechanism.It is also applicable to parametric models and non-parametric models.Because of the flexibility of statistical inference and the combination of prior information,its actual results are more accurate and are favored by many statisticians.In recent years,with the continuous enhancement of computer performance and the continuous improvement of sampling technology,it has solved In addition to the large amount of calculation and the difficulty of calculation,Bayesian method is more and more easily implemented in practical applications,and it has been widely used by statisticians.This paper adopts Bayesian method to deal with some practical issues: Bayesian variable selection of regression model under dependent error.First,this article introduces the statistical analysis of regression model and autoregression model.Based on the research results of statisticians,the dependent errors are applied to the regression model and autoregression model to construct the REGAR model(Regression Autoregression Model)and AR-AR(Autoregression Autoregression)respectively.Model)model,based on the EM algorithm,proposes a new Bayesian variable selection method,referred to as EMVS,which introduces the "spike and slab" prior to determine the maximum posterior estimate of parameters(MAP),and then an additional threshold parameter is used to estimate the indicative variable to obtain the coefficient estimate.This method not only has the characteristics of high model recognition rate,but also has a relatively small amount of calculation.Comparing the simulation results of the Bayesian variable selection of the regression model under dependent errors with the dependent error Lasso,it is concluded that the Bayesian method is better than the Lasso method.Finally,the Bayesian variable selection of the regression model under dependent errors is applied to practice.It also uses the panel data of the national money supply from2013 to 2019 and its influencing factors.Through the Bayesian variable selection of the regression model under dependent error,the factors that affect the money supply are determined: The influencing factors include money supply and fuel commodity price index,consumer price index,quasi-money supply(100 million yuan),and national fiscal revenue(100 million yuan).