Epistemic confidence in the observed confidence interval
本文探讨在频率统计中，观测到的置信区间能否具有认知置信度，通过扩展荷兰赌论证和似然原理，证明基于完全似然的置信度可避免被外部利用，从而具有认知性。
Abstract We define confidence to be epistemic if it applies to an observed confidence interval. Epistemic confidence is unavailable—or even denied—in orthodox frequentist inference, as the confidence level is understood to apply to the procedure. Yet there are obvious practical and psychological needs to think about the uncertainty in the observed interval. We extend the Dutch Book argument used in the classical Bayesian justification of subjective probability to a stronger market‐based version, which prevents external agents from exploiting unused information in any relevant subset. We previously showed that confidence is an extended likelihood, and the likelihood principle states that the likelihood contains all the information in the data, hence leaving no relevant subset. Intuitively, this implies that confidence associated with the full likelihood is protected from the Dutch Book, and hence is epistemic. Our goal is to validate this intuitive notion through theoretical backing and practical illustrations.