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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | https://arxiv.org/abs/2303.11290 |
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| _version_ | 1866909194144186368 |
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| author | Berns, Lukas |
| author_facet | Berns, Lukas |
| contents | In various high-energy physics contexts, such as neutrino-oscillation experiments, several assumptions underlying the typical asymptotic confidence interval construction are violated, such that one has to resort to computationally expensive methods like the Feldman-Cousins method for obtaining confidence intervals with proper statistical coverage. By construction, the computation of intervals at high confidence levels requires fitting millions or billions of pseudo-experiments, while wasting most of the computational cost on overly precise intervals at low confidence levels. In this work, a simple importance sampling method is introduced which reuses pseudo-experiments produced for all tested parameter values in a single mixture distribution. This results in a significant error reduction on the estimated critical values, especially at high confidence levels, and simultaneously yields a correct interpolation of these critical values between the parameter values at which the pseudo-experiments were produced. The theoretically calculated performance is demonstrated numerically using a simple example from the analysis of neutrino oscillations. The relationship to similar techniques applied in statistical mechanics and $p$-value computations is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11290 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An importance sampling method for Feldman-Cousins confidence intervals Berns, Lukas High Energy Physics - Experiment Data Analysis, Statistics and Probability In various high-energy physics contexts, such as neutrino-oscillation experiments, several assumptions underlying the typical asymptotic confidence interval construction are violated, such that one has to resort to computationally expensive methods like the Feldman-Cousins method for obtaining confidence intervals with proper statistical coverage. By construction, the computation of intervals at high confidence levels requires fitting millions or billions of pseudo-experiments, while wasting most of the computational cost on overly precise intervals at low confidence levels. In this work, a simple importance sampling method is introduced which reuses pseudo-experiments produced for all tested parameter values in a single mixture distribution. This results in a significant error reduction on the estimated critical values, especially at high confidence levels, and simultaneously yields a correct interpolation of these critical values between the parameter values at which the pseudo-experiments were produced. The theoretically calculated performance is demonstrated numerically using a simple example from the analysis of neutrino oscillations. The relationship to similar techniques applied in statistical mechanics and $p$-value computations is discussed. |
| title | An importance sampling method for Feldman-Cousins confidence intervals |
| topic | High Energy Physics - Experiment Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2303.11290 |