摘要

本文將以多元線性迴歸模式為研究對象;利用貝氏變數選擇法探討此模式自變數的取捨。 首先，假設隨機誤差矩陣的每一列均具有均數O ，離勢矩陣?的p元常態分配;在此?為pxp 的隨機矩陣，其事前機率分配與│?-1/2(p+1)│成正比。給定參數矩陣和?之後，依變量有p 元常態分配;在此參數矩陣亦為隨機矩陣並和?獨立。原模式中，每一個將被刪除之自變數所對應的參數向量均具有均勻散佈和些許機率集中於O 點的混合事前分配。即所謂的突平分配。有了前面的假設p 可算出每個子模式的事前分自己，繼而導出每個子模式的事後分自己。藉著每個子模式之事後分配求得每個參數向量為O 的事後分配、模式的事後期望項數及所有子模式事後分配的一致性;其為選擇自變數的準則。

若每個多數向量有相同的事前分自己，則參數向量等於O的事?去分自己，模式的事後期望項數，所有子模式事後分配的一致性三者均為勻的函數， γ 就是突高與平高的比。使用貝氏交互效度法得到預測誤差，以預測誤差評估寸。

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