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Implementing errors on errors: Bayesian vs frequentist

delete2025-09-18
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OA
AI
S
Satoshi Mishima
K
Kin-ya Oda
DOI：10.1140/epjc/s10052-025-14638-4delete
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Abstract

Abstract

En 中文
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.

Journal

European Physical Journal C cover
European Physical Journal C
IF:
4.8
Papers:
1.9W
Citations:
4.7W

Organization

D
department of information and mathematical sciences
Scholars:
1
Papers: 1
Citations: 0
D
department of liberal arts
Scholars:
10
Papers: 11
Citations: 0
Cited Papers

Cited Papers

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Statistical models with uncertain error parameters
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Effect of Systematic Uncertainty Estimation on the Muong- 2 Anomaly
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Measuring σ8 using DESI Legacy Imaging Surveys Emission-Line galaxies and Planck CMB lensing, and the impact of dust on parameter inference
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