线性回归模型的Bayes统计推断

Bayesian Statistical Inference of Linear Regression Model

Bayes方法虽融合了样本信息和先验信息,但利用的先验信息都是有历史经验和专家估计所得,因此可靠度不高。该文研究了正态线性回归模型:Y=Xβ+e,e～N(0,σ2In),其中σ2已知,β为未知参数向量,对传统的Bayes方法进行了改进,即把Bayes方法中的后验信息作为改进Bayes的无验信息并融合样本信息进行统计推断,在二次损失函数下得到了β的改进的Bayes估计。由于改进的Bayes方法的先验信息中有样本信息,因此其准确度比传统的Bayes方法准确度更高。

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, σ^2 In ）, σ^2 is known and β is unknown parameter vector. The anther 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 informarion of improved Bayesian methods have sample information, so its accuracy is higher than traditional ones.