Encompassing and Specificity
提出涵盖性的一般概念,涵盖经典和贝叶斯视角,并引入特异性衡量缺乏涵盖的程度,讨论检验方法并与贝叶斯后验几率比较。
A model M is said to encompass another model N if the former can explain the results obtained by the latter. In this paper, we propose a general notion of encompassing that covers both classical and Bayesian viewpoints and essentially represents a concept of sufficiency among models. We introduce the parent notion of specificity that aims at measuring lack of encompassing. Tests for encompassing are discussed and the test statistics are compared to Bayesian posterior odds. Operational approximations are offered to cover situations where exact solutions cannot be obtained.