THE APPLICATION OF COMPUTATIONAL ALGEBRAIC GEOMETRY TO THE ANALYSIS OF DESIGNED EXPERIMENTS: A CASE STUDY

Computational algebraic geometry can be used to solve estimability/identifiability problems in the design of experiments. The key is to replace the design as a set of points by the polynomials whose solutions are the design points. The theory and application of Gröbner bases allows one to find a unique saturated model for each so-called monomial ordering of the independent factors. A case study in engine mapping is fully worked out and employs a simple plotting method for modelling.