{"title":"多项式模型的可识别性源自第一原理和格伯纳基础方法","authors":"Janet D. Godolphin, James D. E. Grant","doi":"arxiv-2409.07062","DOIUrl":null,"url":null,"abstract":"The relationship between a set of design points and the class of hierarchical\npolynomial models identifiable from the design is investigated. Saturated\nmodels are of particular interest. Necessary and sufficient conditions are\nderived on the set of design points for specific terms to be included in leaves\nof the statistical fan. A practitioner led approach to building hierarchical\nsaturated models that are identifiable is developed. This approach is compared\nto the method of model building based on Gr\\\"{o}bner bases. The main results\nare illustrated by examples.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"8 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Identifiability of Polynomial Models from First Principles and via a Gröbner Basis Approach\",\"authors\":\"Janet D. Godolphin, James D. E. Grant\",\"doi\":\"arxiv-2409.07062\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The relationship between a set of design points and the class of hierarchical\\npolynomial models identifiable from the design is investigated. Saturated\\nmodels are of particular interest. Necessary and sufficient conditions are\\nderived on the set of design points for specific terms to be included in leaves\\nof the statistical fan. A practitioner led approach to building hierarchical\\nsaturated models that are identifiable is developed. This approach is compared\\nto the method of model building based on Gr\\\\\\\"{o}bner bases. The main results\\nare illustrated by examples.\",\"PeriodicalId\":501379,\"journal\":{\"name\":\"arXiv - STAT - Statistics Theory\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - STAT - Statistics Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.07062\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - STAT - Statistics Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07062","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Identifiability of Polynomial Models from First Principles and via a Gröbner Basis Approach
The relationship between a set of design points and the class of hierarchical
polynomial models identifiable from the design is investigated. Saturated
models are of particular interest. Necessary and sufficient conditions are
derived on the set of design points for specific terms to be included in leaves
of the statistical fan. A practitioner led approach to building hierarchical
saturated models that are identifiable is developed. This approach is compared
to the method of model building based on Gr\"{o}bner bases. The main results
are illustrated by examples.