Summary
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.
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5 Acknowledgments
The authors wish to thank the CoCoA group in Genova, Italy for their help with the use of the package. The last two authors acknowledge the support of the UK Engineering and Physical Science Research Council. The case study was also supported by EPSRC as part of a CASE award in collaboration with Ford Motor Co. Ltd.
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Appendices
A CoCoA code
B Maple code
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Holliday, T., Pistone, G., Riccomagno, E. et al. The application of computational algebraic geometry to the analysis of designed experiments: a case study. Computational Statistics 14, 213–231 (1999). https://doi.org/10.1007/s001800050014
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DOI: https://doi.org/10.1007/s001800050014