A Possibility-Theoretic Solution to Basu’s Bayesian–Frequentist Via Media

Ryan Martin ()
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Ryan Martin: North Carolina State University

Sankhya A: The Indian Journal of Statistics, 2024, vol. 86, issue 1, No 4, 43-70

Abstract: Abstract Basu’s via media is what he referred to as the middle road between the Bayesian and frequentist poles. He seemed skeptical that a suitable via media could be found, but I disagree. My basic claim is that the likelihood alone can’t reliably support probabilistic inference, and I justify this by considering a technical trap that Basu stepped in concerning interpretation of the likelihood. While reliable probabilistic inference is out of reach, it turns out that reliable possibilistic inference is not. I lay out my proposed possibility-theoretic solution to Basu’s via media and I investigate how the flexibility afforded by my imprecise-probabilistic solution can be leveraged to achieve the likelihood principle (or something close to it).

Keywords: Conditional inference; fiducial argument; imprecise probability; inferential model; likelihood principle; validity (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13171-023-00323-9

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