The conditionality principle $C$ plays a key role in attempts to characterize the concept of statistical evidence. The standard version of $C$ considers a model and a derived conditional model, formed by conditioning on an ancillary statistic for the model, together with the data, to be equivalent with respect to their statistical evidence content. This equivalence is considered to hold for any ancillary statistic for the model but creates two problems. First, there can be more than one maximal ancillary in a given context and this leads to $C$ not being an equivalence relation and, as such, calls into question whether $C$ is a proper characterization of statistical evidence. Second, a statistic $A$ can change from ancillary to informative (in its marginal distribution) when another ancillary $B$ changes, from having one known distribution $P_{B},$ to having another known distribution $Q_{B}.$ This means that the stability of ancillarity differs across ancillary statistics and raises the issue of when a statistic can be said to be truly ancillary. It is therefore natural, and practically important, to limit conditioning to the set of ancillaries whose distribution is irrelevant to the ancillary status of any other ancillary statistic. This results in a family of ancillaries for which there is a unique maximal member. This also gives a new principle for inference, the stable conditionality principle, that satisfies the criteria required for any principle whose aim is to characterize statistical evidence.
翻译:条件性原则$C$在试图确定统计证据概念的特点方面起着关键作用。标准版本$C$认为一个模型和衍生的有条件模型,该模型以该模型的辅助统计数据和数据为条件,形成了一个模型和衍生的有条件模型,在统计证据内容方面与该模型的任何辅助统计数据相等。这一等值被认为适用于该模型的任何辅助统计数据,但造成了两个问题。首先,在特定背景下,可能存在不止一个最高辅助因素,这导致一个最高辅助因素在某种情况下可能不是一个对等关系,因此,质疑美元是否是对统计证据的适当定性。第二,当另一个辅助B$的变动,从已知的分发量$P ⁇ B}到另一个已知的分发量美元等值,将美元作为辅助因素(在其边际分布中)形成一个衍生要素时,一个美元统计值可以改变为信息性(从附带要素改为信息性模式),因为另一个辅助值的变动,从已知的分发量为$P ⁇ B},到另外一个已知的分发量值为$B}产生两个问题。这意味着,在某个辅助统计数据的稳定性的稳定性问题何时可以说是真正的辅助性关系,因此,将限制其分配与辅助性原则的调节性是必然和最高性原则。这个原则,这是一个核心性原则的必然的结果。