An imprecise-probabilistic characterization of frequentist statistical inference

Ryan Martin

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arXiv · 2112.10904

An imprecise-probabilistic characterization of frequentist statistical inference

Ryan Martin

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Abstract

Between the two dominant schools of thought in statistics, namely, Bayesian and classical/frequentist, a main difference is that the former is grounded in the mathematically rigorous theory of probability while the latter is not. In this paper, I show that the latter is grounded in a different but equally mathematically rigorous theory of imprecise probability. Specifically, I show that for every suitable testing or confidence procedure with error rate control guarantees, there exists a consonant plausibility function whose derived testing or confidence procedure is no less efficient. Beyond its foundational implications, this characterization has at least two important practical consequences: first, it simplifies the interpretation of p-values and confidence regions, thus creating opportunities for improved education and scientific communication; second, the constructive proof of the main results leads to a strategy for new and improved methods in challenging inference problems.

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Ryan Martin. 2021-12-20. An imprecise-probabilistic characterization of frequentist statistical inference. https://arxiv.org/abs/2112.10904

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