We relate scattering amplitudes in particle physics to maximum likelihood estimation for discrete models in algebraic statistics. The scattering potential plays the role of the log-likelihood function, and its critical points are solutions to rational function equations. We study the ML degree of low-rank tensor models in statistics, and we revisit physical theories proposed by Arkani-Hamed, Cachazo and their collaborators. Recent advances in numerical algebraic geometry are employed to compute and certify critical points. We also discuss positive models and how to compute their string amplitudes.

翻译：我们把粒子物理学中的散射振幅与对代数统计中离散模型的最大可能性估计联系起来。 散射潜能发挥日志相似功能的作用, 其临界点是理性函数方程式的解决方案。 我们研究了低度振幅模型在统计中的 ML 度, 我们重新审视了阿卡尼- 哈迈德、 卡查佐及其合作者提出的物理理论。 数字代数几何学的最新进展被用于计算和验证临界点。 我们还讨论了正值模型以及如何计算其字符串振幅 。