Identifiability of Polynomial Models from First Principles and via a Gröbner Basis Approach

Janet D. Godolphin, James D. E. Grant
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Abstract

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.
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多项式模型的可识别性源自第一原理和格伯纳基础方法
研究了一组设计点与可从设计中识别的分层多项式模型类别之间的关系。饱和模型尤其值得关注。研究得出了设计点集合的必要条件和充分条件,以便在统计扇叶中包含特定项。开发了一种由实践者主导的方法来建立可识别的分层饱和模型。这种方法与基于 Gr\"{o}bner 基的模型构建方法进行了比较。通过实例说明了主要结果。
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