Year: 2026
Type: article
Abstract: Classical statistical methods have theoretical justification when the sample size is predetermined. In applications, however, sample sizes are often data-dependent rather than predetermined. The aforementioned methods aren’t reliable in this latter case, hence the recent interest in e-processes and methods that are anytime valid, i.e., reliable for any dynamic data-collection plan. But if the investigator has relevant-yet-incomplete prior information about the quantity of interest, then there’s an opportunity for efficiency gain. This paper proposes a regularized e-process framework featuring a knowledge-based, imprecise-probabilistic regularization with improved efficiency. A generalized version of Ville’s inequality is established, ensuring that inference based on the regularized e-process is anytime valid in a novel, knowledge-dependent sense. Regularized e-processes also facilitate possibility-theoretic uncertainty quantification with strong frequentist-like calibration properties and other Bayesian-like properties: satisfies the likelihood principle, avoids sure-loss, and offers formal decision-making with reliability guarantees.
Source: Bernoulli
DOI: 10.3150/25-bej1939
Author: Ryan Martin
Institution: North Carolina State University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4403883822