تقرير
Maximum Likelihood Degrees of Brownian Motion Tree Models: Star Trees and Root Invariance
| العنوان: | Maximum Likelihood Degrees of Brownian Motion Tree Models: Star Trees and Root Invariance |
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| المؤلفون: | Coons, Jane Ivy, Cox, Shelby, Maraj, Aida, Nometa, Ikenna |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Quantitative Biology Statistics |
| مصطلحات موضوعية: | Mathematics - Statistics Theory, Mathematics - Algebraic Geometry, Quantitative Biology - Populations and Evolution, 62R01, 14M25, 62F10 |
| الوصف: | A Brownian motion tree (BMT) model is a Gaussian model whose associated set of covariance matrices is linearly constrained according to common ancestry in a phylogenetic tree. We study the complexity of inferring the maximum likelihood (ML) estimator for a BMT model by computing its ML-degree. Our main result is that the ML-degree of the BMT model on a star tree with $n + 1$ leaves is $2^{n+1}-2n-3$, which was previously conjectured by Am\'endola and Zwiernik. We also prove that the ML-degree of a BMT model is independent of the choice of the root. The proofs rely on the toric geometry of concentration matrices in a BMT model. Toward this end, we produce a combinatorial formula for the determinant of the concentration matrix of a BMT model, which generalizes the Cayley-Pr\"ufer theorem to complete graphs with weights given by a tree. Comment: 19 pages, 3 figures. Comments welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.10322 |
| رقم الأكسشن: | edsarx.2402.10322 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |