Moment varieties of the inverse Gaussian and gamma distributions are nondefective
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909641970024448 |
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| author | Henriksson, Oskar Ranestad, Kristian Seccia, Lisa Yu, Teresa |
| author_facet | Henriksson, Oskar Ranestad, Kristian Seccia, Lisa Yu, Teresa |
| contents | We show that the parameters of a $k$-mixture of inverse Gaussian or gamma distributions are algebraically identifiable from the first $3k-1$ moments, and rationally identifiable from the first $3k+2$ moments. Our proofs are based on Terracini's classification of defective surfaces, careful analysis of the intersection theory of moment varieties, and a recent result on sufficient conditions for rational identifiability of secant varieties by Massarenti--Mella. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_18421 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moment varieties of the inverse Gaussian and gamma distributions are nondefective Henriksson, Oskar Ranestad, Kristian Seccia, Lisa Yu, Teresa Algebraic Geometry Statistics Theory 62R01, 14C17, 14N05, 14N07, 14M12 We show that the parameters of a $k$-mixture of inverse Gaussian or gamma distributions are algebraically identifiable from the first $3k-1$ moments, and rationally identifiable from the first $3k+2$ moments. Our proofs are based on Terracini's classification of defective surfaces, careful analysis of the intersection theory of moment varieties, and a recent result on sufficient conditions for rational identifiability of secant varieties by Massarenti--Mella. |
| title | Moment varieties of the inverse Gaussian and gamma distributions are nondefective |
| topic | Algebraic Geometry Statistics Theory 62R01, 14C17, 14N05, 14N07, 14M12 |
| url | https://arxiv.org/abs/2409.18421 |