Application Of Bayesian Method Based On Linear Regression Model

Linear regression model is a very important part of regression analysis.It is widely used in practical problems in many fields.It is simple and convenient to describe the linear relationship between things.Bayesian theory also occupies an important position in statistics.Although the research in China started late,it has been a hot research issue in recent years.Therefore,this paper mainly focuses on the linear regression model,Bayesian theory,and the correlation between the two.Combined research.In the study of linear regression models,this paper mainly uses multiple linear regression models and logistic regression models.Starting from the general form of the two models,to the characteristics of the two models themselves,as well as the conditions for establishing and testing the models,explained in great detail,and then solved the model's maximum likelihood estimation results.This article takes 379 college students who have received innovation competition awards in a university as an example to make a statistical analysis of the problems affecting college students' innovation ability.The results are feasible and effective.This paper combines a linear regression model with Bayesian theory.In the Bayesian multiple linear regression model,a prior without information is selected as the prior distribution of the model,and the corresponding Bayesian theoretical parameter estimation results are obtained through theoretical derivation;In the logistic regression model,the joint normal prior distribution is selected as the prior distribution of the model to obtain the parameter estimates in the model,and equation constraints are also added to the logistic model to reduce the corresponding parameters to be estimated in different problems.Number,which makes the model parameters easy to solve.Bayesian theory combines sample information,prior information,and overall information to solve the parameters in the model,and obtains the theoretical estimation results of the parameters,which proves that the method is effective.Finally,this paper uses numerical simulation methods to simulate the maximum likelihood estimation of the parameters in the linear regression model and the Bayesian parameter estimation to obtain the estimation results.In the uniform distribution and multiple linear regression models,the maximum similarity of the parameters is compared.Ran estimation and Bayesian parameter estimation,the obtained Bayesian parameter estimation has higher accuracy and smaller deviation.Therefore,the Bayesian linear regression model is effective and better.