{"title":"似然方程和散射振幅","authors":"B. Sturmfels, Simon Telen","doi":"10.2140/astat.2021.12.167","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":41066,"journal":{"name":"Journal of Algebraic Statistics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"30","resultStr":"{\"title\":\"Likelihood equations and scattering amplitudes\",\"authors\":\"B. Sturmfels, Simon Telen\",\"doi\":\"10.2140/astat.2021.12.167\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":41066,\"journal\":{\"name\":\"Journal of Algebraic Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-12-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"30\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebraic Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/astat.2021.12.167\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/astat.2021.12.167","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.