Bayesian Statistical Inference of Linear Regression Model

Although Bayesian methods merge the samples information with prior information,but the use of a prior information is historical experience and experts estimate so that the reliability is not high.This paper studies the normal linear regression model:Y=Xβ+e,e～N(0,σ2In),σ2 is known and β is unknown parameter vector.The auther improve traditional Bayesian methods,treating posterior information as the improved Bayesian methods' prior information and integrating samples information again.under the second loss of function,we could get a modified Bayesian estimation of β.Due to the prior information of improved Bayesian methods have sample information,so its accuracy is higher than traditional ones.