Improved Asymptotic Formulae for Statistical Interpretation Based on Likelihood Ratio Tests
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866908468722532352 |
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| author | Xia, Li-Gang Zhang, Yan |
| author_facet | Xia, Li-Gang Zhang, Yan |
| contents | In this work, we attempt to refine the classic asymptotic formulae to describe the probability distribution of likelihood-ratio statistical tests. The idea is to split the probability distribution function into two parts. One part is universal and described by the asymptotic formulae. The other part is case-dependent and is estimated explicitly using a 6-bin model proposed in this work. The latter is similar to performing toy simulations and can therefore predict the discrete structures in the probability distributions. The new asymptotic formulae provide a much better differential description of the test statistics. This improved performance is demonstrated in two toy examples for common likelihood ratio statistics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_06944 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Improved Asymptotic Formulae for Statistical Interpretation Based on Likelihood Ratio Tests Xia, Li-Gang Zhang, Yan Data Analysis, Statistics and Probability High Energy Physics - Experiment In this work, we attempt to refine the classic asymptotic formulae to describe the probability distribution of likelihood-ratio statistical tests. The idea is to split the probability distribution function into two parts. One part is universal and described by the asymptotic formulae. The other part is case-dependent and is estimated explicitly using a 6-bin model proposed in this work. The latter is similar to performing toy simulations and can therefore predict the discrete structures in the probability distributions. The new asymptotic formulae provide a much better differential description of the test statistics. This improved performance is demonstrated in two toy examples for common likelihood ratio statistics. |
| title | Improved Asymptotic Formulae for Statistical Interpretation Based on Likelihood Ratio Tests |
| topic | Data Analysis, Statistics and Probability High Energy Physics - Experiment |
| url | https://arxiv.org/abs/2101.06944 |