On Resolving Problems with Conditionality and Its Implications for Characterizing Statistical Evidence

Abstract The conditionality principle C plays a key role in attempts to characterize the concept of statistical evidence. standard version considers model and derived conditional model, formed by conditioning on an ancillary statistic for together with data, be equivalent respect their evidence content. This equivalence is considered hold any but creates two problems. First, there can more than one maximal given context this leads not being relation and, as such, calls into question whether proper characterization Second, A change from informative (in its marginal distribution) when another B changes, having known distribution P , Q . means that stability ancillarity differs across statistics raises issue said truly ancillary. It therefore natural, practically important, limit set ancillaries whose irrelevant status other statistic. results family which unique member. also gives new inference, stable principle, satisfies criteria required aim