Likelihood Correspondence of Toric Statistical Models
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915023716089856 |
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| author | Barnhill, David Cobb, John Faust, Matthew |
| author_facet | Barnhill, David Cobb, John Faust, Matthew |
| contents | Maximum likelihood estimation (MLE) is a fundamental problem in statistics. Characteristics of the MLE problem for discrete algebraic statistical models are reflected in the geometry of the $\textit{likelihood correspondence}$, a variety that ties together data and their maximum likelihood estimators. We construct this ideal for the large class of toric models and find a Gröbner basis in the case of complete and joint independence models arising from multi-way contingency tables. All of our constructions are implemented in $\textit{Macaulay2}$ in a package $\texttt{LikelihoodGeometry}$ along with other tools of use in algebraic statistics. We end with an experimental section using these implementations on several interesting examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08501 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Likelihood Correspondence of Toric Statistical Models Barnhill, David Cobb, John Faust, Matthew Statistics Theory Commutative Algebra Algebraic Geometry 62R01, 13P25, 14N99 Maximum likelihood estimation (MLE) is a fundamental problem in statistics. Characteristics of the MLE problem for discrete algebraic statistical models are reflected in the geometry of the $\textit{likelihood correspondence}$, a variety that ties together data and their maximum likelihood estimators. We construct this ideal for the large class of toric models and find a Gröbner basis in the case of complete and joint independence models arising from multi-way contingency tables. All of our constructions are implemented in $\textit{Macaulay2}$ in a package $\texttt{LikelihoodGeometry}$ along with other tools of use in algebraic statistics. We end with an experimental section using these implementations on several interesting examples. |
| title | Likelihood Correspondence of Toric Statistical Models |
| topic | Statistics Theory Commutative Algebra Algebraic Geometry 62R01, 13P25, 14N99 |
| url | https://arxiv.org/abs/2312.08501 |