Implementing Errors on Errors: Bayesian vs Frequentist
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913998970028032 |
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| author | Mishima, Satoshi Oda, Kin-ya |
| author_facet | Mishima, Satoshi Oda, Kin-ya |
| contents | When combining apparently inconsistent experimental 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_06521 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Implementing Errors on Errors: Bayesian vs Frequentist Mishima, Satoshi Oda, Kin-ya High Energy Physics - Phenomenology Instrumentation and Methods for Astrophysics High Energy Physics - Experiment Methodology When combining apparently inconsistent experimental 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. |
| title | Implementing Errors on Errors: Bayesian vs Frequentist |
| topic | High Energy Physics - Phenomenology Instrumentation and Methods for Astrophysics High Energy Physics - Experiment Methodology |
| url | https://arxiv.org/abs/2505.06521 |