https://doi.org/10.1140/epjc/s10052-025-14638-4
Letter
Implementing errors on errors: Bayesian vs frequentist
1
Department of Liberal Arts, Saitama Medical University, 350-0495, Saitama, Japan
2
Department of Information and Mathematical Sciences, Tokyo Woman’s Christian University, 167-8585, Tokyo, Japan
Received:
16
May
2025
Accepted:
10
August
2025
Published online:
18
September
2025
When combining apparently inconsistentexperimental results, one often implements errors on errors. The Particle Data Group’s phenomenological prescription offers a practical solution but lacks a firm theoretical foundation. To address this, D’Agostini and Cowan have proposed Bayesian and frequentist approaches, respectively, both introducing gamma-distributed auxiliary variables to model uncertainty in quoted errors. In this Letter, we show that these two formulations admit a parameter-by-parameter correspondence, and are structurally equivalent. This identification clarifies how Bayesian prior choices can be interpreted in terms of frequentist sampling assumptions, providing a unified probabilistic framework for modeling uncertainty in quoted variances.
© The Author(s) 2025
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