Details:
Title  Generalised confounding with Gröbner bases  Author(s)  Giovanni Pistone, Henry P. Wynn  Type  Article in Journal  Abstract  Many problems of confounding and identifiability for polynomial and multidimensional polynomial models can be solved using methods of algebraic geometry aided by the fact that modern computational algebra packages such as MAPLE can be used. The problem posed here is to give a description of the identifiable models given a particular experimental design. The method is to represent the design as a variety V, namely the solution of a set of algebraic equations. An equivalent description is the corresponding ideal I which is the set of all polynomials which are zero on the design points. Starting with a class of models M the quotient vector space M/I yields a class of identifiable monomial terms of the models. The theory of Grobner bases is used to characterise the design ideal and the quotient. The theory is tested using some simple examples, including the popular L18 design.  Keywords  computational algebraic geometry, experimetnal design, Grobner basis, identifiability  Copyright  Biometrika Trust 
URL 
dx.doi.org/10.1093/biomet/83.3.653 
Language  English  Journal  Biometrika  Volume  83  Pages  653666  Year  1996  Month  September  Translation 
No  Refereed 
No 
