Generalised confounding with Grobner bases

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 Gröbner bases is used to characterise the design ideal and the quotient. The theory is tested using some simple examples, including the popular LI8 design.