Kappa先驗分配的選取暨貝氏統計推論

Abstract

Cohen's Kappa 是一個被廣泛應用的一致性量測。本文主要探討如何利用貝氏統計方法來估計兩位判讀者之間的一致性程度，此時假設資料為二元分類判讀結果，並假設兩位判讀者判讀為正的機率相同。本文提出兩種Jeffreys' prior來估計kappa，其一為階層式先驗分配 (hierarchical prior)，引進efficient Fisher information概念，求出kappa的條件先驗分配，再配合邊際機率先驗分配的選取來求出kappa眾數估計值；其二則直接利用聯合先驗分配求出kappa估計值。一般而言，兩者的貝氏估計值非常接近。另外，由模擬結果也顯示，利用貝氏方法求出的估計值較傳統最大概似估計值(MLE)接近真值，再者，利用貝氏方法也可藉由先驗分配的設定來解決過去文獻中稱之為悖論 (paradox) 的問題。

Cohen's kappa is a popular index to measure the beyond-chance agreement. In this thesis, I propose a Bayesian approach to study the agreement for the case of two raters with binary ratings in the setting of reliability test. In other words, I focus on the kappa under the assumption of equal marginal probability of positive classification. Two kinds of Jeffreys' priors are used in inference. One is a hierarchical prior based on efficient Fisher information, and the other is a joint prior based on Fisher information matrix. In general, the resulting two estimators of posterior mode of kappa are very similar. Simulation studies with small and moderate sample size are conducted to evaluate the performance of two Bayesian estimators and MLE. Results show that the posterior mode of kappa based on efficient Fisher information is the best among three estimators. In addition, it is recommended to use a non-informative prior for in most cases. Bayesian method can handle easily even some special data.