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.

中文翻译：

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观察到的置信区间的认知置信度

如果置信度适用于观察到的置信区间，我们将其定义为认知置信度。在正统的频率论推理中，认知置信度是不可用的，甚至被否认，因为置信度被理解为适用于该过程。然而，显然存在实际和心理上的需要来考虑观察到的区间的不确定性。我们将主观概率的经典贝叶斯论证中使用的 Dutch Book 论证扩展到更强大的基于市场的版本，这可以防止外部代理利用任何相关子集中未使用的信息。我们之前表明置信度是扩展的似然性，似然性原理指出似然性包含数据中的所有信息，因此不留下相关子集。直观上，这意味着与完全可能性相关的置信度受到荷兰书的保护，因此是认知性的。我们的目标是通过理论支持和实践说明来验证这个直观的概念。