從貝氏觀點診斷離群值及具有影響力之觀察值

Abstract

在線性迴歸分析中，資料的不適當，常導致研究者選擇了不當的模式，為避免此缺失，在分析資料前須先做好診斷工作。本文中將從貝氏觀點提出一些不同的診斷方法以供參考。首先推導出均數移動參數a=(a₁,…,a_k)`的事後分配，並利用a`a/k的事後均數診斷出不當資料點。接著，考慮在個別模式下以β事後分配之總變異及廣義變異為標準，診斷出離群值及具有潛在影響力之觀測值。最後，分別利用(i)β的事後分配(ii)σ²的事後分配(iii)(β,σ²)的聯合事後分配，推導出對應的對稱均方差以做為診斷標準。

In this thesis, some different diagnostic methodologies for outliers and influential observations from Bayesian point of view are proposed. We firstly derive the marginal posterior distribution of the mean-shift parameter a=(a₁,a_k)¹, then use the posterior mean of a¹a/k to detect the spurious data items. Secondly, we use the posterior total variance and generalized variance of β as diagnostic criterions for outliers and influential observations. Finally, we utilize (i) the posterior distribution of β, (ii) the posterior distribution of σ², and (iii) the joint posterior distribution of β, σ² to find their corresponding symmetric mean square differences , which can be used as diagnostic criterions.