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We use a logical device called the Dutch Book to establish epistemicconfidence, defined as the sense of confidence \emph{in an observed} confidenceinterval. This epistemic property is unavailable -- or even denied -- inorthodox frequentist inference. In financial markets, including the bettingmarket, the Dutch Book is also known as arbitrage or risk-free profitabletransaction. A numerical confidence is deemed epistemic if its use as a bettingprice is protected from the Dutch Book by an external agent. Theoretically, toconstruct the Dutch Book, the agent must exploit unused information availablein any relevant subset. Pawitan and Lee (2021) showed that confidence is anextended likelihood, and the likelihood principle states that the likelihoodcontains all the information in the data, hence leaving no relevant subset.Intuitively, this implies that confidence associated with the full likelihoodis protected from the Dutch Book, and hence is epistemic. Our aim is to providethe theoretical support for this intuitive notion.

Epistemic confidence, the Dutch Book and relevant subsets