2021/04/30 by Yudi Pawitan, Pawitan, Yudi, Hangbin Lee +3
Arts and Humanities · Decision Sciences · Mathematics · #Decision-Making and Behavioral Economics #FOS: Mathematics #Philosophy and History of Science #Probability and Statistical Research #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2104.14712
openalex publication_date 2021/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use a logical device called the Dutch Book to establish epistemic confidence, defined as the sense of confidence 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.