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

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  • Ryan Martin

    (North Carolina State University)

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).

Suggested Citation

  • Ryan Martin, 2024. "A Possibility-Theoretic Solution to Basu’s Bayesian–Frequentist Via Media," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 43-70, November.
    • Handle: RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00323-9
    DOI: 10.1007/s13171-023-00323-9
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    References listed on IDEAS

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    1. Dubois, Didier, 2006. "Possibility theory and statistical reasoning," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 47-69, November.
    2. Ryan Martin & Chuanhai Liu, 2013. "Inferential Models: A Framework for Prior-Free Posterior Probabilistic Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 301-313, March.
    3. Jan Hannig & Hari Iyer & Randy C. S. Lai & Thomas C. M. Lee, 2016. "Generalized Fiducial Inference: A Review and New Results," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1346-1361, July.
    4. Jan Hannig & Thomas C. M. Lee, 2009. "Generalized fiducial inference for wavelet regression," Biometrika, Biometrika Trust, vol. 96(4), pages 847-860.
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