Epistemic confidence, the Dutch Book and relevant subsets

TL;DR

This paper explores how the Dutch Book concept can establish epistemic confidence in observed confidence intervals, contrasting with orthodox methods, and demonstrates that confidence linked to the full likelihood is protected from Dutch Book exploitation.

Contribution

It provides theoretical support showing that confidence based on the full likelihood is epistemic and protected from Dutch Book exploitation, unlike traditional frequentist confidence.

Findings

Likelihood contains all relevant information, leaving no relevant subset.

Confidence based on the full likelihood is protected from Dutch Book.

Theoretical link between likelihood principle and epistemic confidence.

Abstract

We use a logical device called the Dutch Book to establish epistemic confidence, defined as the sense of confidence \emph{in an observed} confidence interval. This epistemic property is unavailable -- or even denied -- in orthodox frequentist inference. In financial markets, including the betting market, the Dutch Book is also known as arbitrage or risk-free profitable transaction. A numerical confidence is deemed epistemic if its use as a betting price is protected from the Dutch Book by an external agent. Theoretically, to construct the Dutch Book, the agent must exploit unused information available in any relevant subset. Pawitan and Lee (2021) 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 aim is to provide the theoretical support for this intuitive notion.