Methodological considerations for semialgebraic hypothesis testing with incomplete U-statistics
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909694711300096 |
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| author | Barnhill, David Garrote-López, Marina Gross, Elizabeth Hill, Max Kagy, Bryson Rhodes, John A. Zhang, Joy Z. |
| author_facet | Barnhill, David Garrote-López, Marina Gross, Elizabeth Hill, Max Kagy, Bryson Rhodes, John A. Zhang, Joy Z. |
| contents | Recently, Sturma, Drton, and Leung proposed a general-purpose stochastic method for hypothesis testing in models defined by polynomial equality and inequality constraints. Notably, the method remains theoretically valid even near irregular points, such as singularities and boundaries, where traditional testing approaches often break down. In this paper, we evaluate its practical performance on a collection of biologically motivated models from phylogenetics. While the method performs remarkably well across different settings, we catalogue a number of issues that should be considered for effective application. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Methodological considerations for semialgebraic hypothesis testing with incomplete U-statistics Barnhill, David Garrote-López, Marina Gross, Elizabeth Hill, Max Kagy, Bryson Rhodes, John A. Zhang, Joy Z. Populations and Evolution Methodology 92D15, 62F03, 62R01 Recently, Sturma, Drton, and Leung proposed a general-purpose stochastic method for hypothesis testing in models defined by polynomial equality and inequality constraints. Notably, the method remains theoretically valid even near irregular points, such as singularities and boundaries, where traditional testing approaches often break down. In this paper, we evaluate its practical performance on a collection of biologically motivated models from phylogenetics. While the method performs remarkably well across different settings, we catalogue a number of issues that should be considered for effective application. |
| title | Methodological considerations for semialgebraic hypothesis testing with incomplete U-statistics |
| topic | Populations and Evolution Methodology 92D15, 62F03, 62R01 |
| url | https://arxiv.org/abs/2507.13531 |