多元线性回归的Bayes假设检验

Bayes Hypothesis Testing of Multivariate Linear Regression Model

对于多元线性回归模型 :Y =Xβ+e ,e～Nn(0 ,σ2 In) ,本文首先讨论了在两种不同先验分布下 β的后验密度 ,其次利用后验密度定义了Rp 与其子集上的最大后验密度比 ,最后作了两个方面的假设检验 :①回归方程的显著性检验 ,HO: β1=β2 =… =βp- 1=0 ;②回归系数的显著性检验 ,H1:βi =0 (i=1,2 ,… ,p - 1) .

In this paper,the unknown parameter β's posterior distribution in the linear model Y=Xβ+e is discussed,where e～N n(0,σ 2I n),then an ratio of β's maximum probability distribution functions in R P and one of its subsets is defined,finally,two special situations are tested:①Hypothesis testing of regression equation,H 0∶ β 1=β 2=...=β P-1 ②Hypothesis testing of regression coefficient,H 1∶ β i=0(i=1,2,,p-1)