Classifying one-dimensional discrete models with maximum likelihood degree one
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866908402272174080 |
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| author | Bik, Arthur Marigliano, Orlando |
| author_facet | Bik, Arthur Marigliano, Orlando |
| contents | We propose a classification of all one-dimensional discrete statistical models with maximum likelihood degree one based on their rational parametrization. We show how all such models can be constructed from members of a smaller class of 'fundamental models' using a finite number of simple operations. We introduce 'chipsplitting games', a class of combinatorial games on a grid which we use to represent fundamental models. This combinatorial perspective enables us to show that there are only finitely many fundamental models in the probability simplex $Δ_n$ for $n\leq 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_09547 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Classifying one-dimensional discrete models with maximum likelihood degree one Bik, Arthur Marigliano, Orlando Combinatorics Algebraic Geometry Statistics Theory 62R01, 05C57, 05E14 We propose a classification of all one-dimensional discrete statistical models with maximum likelihood degree one based on their rational parametrization. We show how all such models can be constructed from members of a smaller class of 'fundamental models' using a finite number of simple operations. We introduce 'chipsplitting games', a class of combinatorial games on a grid which we use to represent fundamental models. This combinatorial perspective enables us to show that there are only finitely many fundamental models in the probability simplex $Δ_n$ for $n\leq 4$. |
| title | Classifying one-dimensional discrete models with maximum likelihood degree one |
| topic | Combinatorics Algebraic Geometry Statistics Theory 62R01, 05C57, 05E14 |
| url | https://arxiv.org/abs/2205.09547 |