Robust Bayesian Analysis And Its Applications For Multivariate Linear Regressive Models

Robustness is a very important concept in statistical inference.Robustness is also an important indica.tor for evaluating the pros and cons of model estimation.Since the conservatism was formally proposed in the 1950s,the concept,type,eval-uation method of robustness and discussion and research on how to achieve robust est,imation has never stopped.Many scholars at home and abroad have used dif-ferent methods to estimate the linear regression model.The multivariate regression model is more susceptible to outliers than the linear regression model.Interference.Therefore,the robust estimation method of multivariate variable regression model is a valuable research direction.In this paper,the robust estimation of linear regression and multi-dependent,variable regression model is studied under Bayesian framework.Based on the ro-bust Bayesian estimation of linear regression model,the Robust Bayesian of multi-dependent regression model is proposed.In the simulation experiment,the robust-ness of the estimation method is evaluated by constructing the correlation statistical indicators and the visualization of the parameter posterior density function.Finally，the model and estimation method in the paper to the study of the relationship be-tween middle students’ sports test scores and physical conditions.The main contents as follows:1.The basic principles of the multivariate regression model and the least squares est,imation method,the related concepts of robustness,the statistical theory related to Bayesian statistical inference and the general Bayesian parameter estimation of multivariate regression model are sorted out.2.The Robust Bayesian method for linear regression model is introduced,and the rela.ted simulation experiments are carried out to verify the robustness of the proposed method.Based on the Robust Bayesian estimation of linear regression model,a Robust Bayesian analysis method for multivariate regression model is pro-posed.Firstly,the conditional posterior distribution of Bayesian multivariate model parameters is derived.Secondly,the approximate posterior distribution of regression coefficients is obtained by Markov chain Monte Carlo(MCMC)sampling method.Finally,it is designed of variety of outliers are generated in numerical simulation experiment,and the related indicators for evaluating robustness and the plots of the posterior density function are constructed to illustrate the robustness of the proposed method.3.The relationship between physical test scores and physical fitness of middle school students was studied.Taking the data of sports test scores of middle school students in more than 10 schools in Xinjiang Uygur Autonomous Region,and mod-eling and analyzing the performance of middle school students’ sports test by using least squares method,ordinary Bayesian method and the Robust Bayesian method proposed in this paper.The robust Bayesian estimation results of some variables are different from the other two methods.The results show that the Robust Bayesian method are more conform with the actual situation.