The Fisher score on the closed simplex
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915784276574208 |
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| author | Pistone, Giovanni Rapallo, Fabio Riccomagno, Eva |
| author_facet | Pistone, Giovanni Rapallo, Fabio Riccomagno, Eva |
| contents | We extend classical analytic tools for finite-state statistical models to allow zero probabilities. Using methods from algebraic statistics and information geometry, we develop a framework in which a smooth statistical model could hit the boundary of the simplex, for example, in contingency tables with non-structural zeros. The central object of our approach is the vector bundle whose fibres are the $p$-contrasts associated to each probability distribution $p$. In this framework, Fisher score and other key statistical concepts, such as entropy for one-dimensional statistical models, admit an algebraic representation also on the boundary of the simplex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07665 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Fisher score on the closed simplex Pistone, Giovanni Rapallo, Fabio Riccomagno, Eva Statistics Theory 2020: 62B11, 62R01, 62H17 We extend classical analytic tools for finite-state statistical models to allow zero probabilities. Using methods from algebraic statistics and information geometry, we develop a framework in which a smooth statistical model could hit the boundary of the simplex, for example, in contingency tables with non-structural zeros. The central object of our approach is the vector bundle whose fibres are the $p$-contrasts associated to each probability distribution $p$. In this framework, Fisher score and other key statistical concepts, such as entropy for one-dimensional statistical models, admit an algebraic representation also on the boundary of the simplex. |
| title | The Fisher score on the closed simplex |
| topic | Statistics Theory 2020: 62B11, 62R01, 62H17 |
| url | https://arxiv.org/abs/2602.07665 |