Holliday, Tim; Pistone, Giovanni; Riccomagno, Eva; Wynn, Henry P. The applications of computational algebraic geometry to the analysis of designed experiments: a case study. (English) Zbl 0933.62070 Comput. Stat. 14, No. 2, 213-231 (1999). This article demonstrates how ideas from algebraic geometry can be introduced to solve certain general problems in the experimental designs for polynomial models. For instance, the present paper discusses following problem: given a particular design deduce a class of models that are estimable with this design. The idea is to replace the natural notion of a design as a set of points in a design space by polynomials whose solutions are the design points. For calculation purposes techniques based on the theory and application of Groebner bases are accessible via computational algebra packages such as Maple and CoCoA. To illustrate the power of the proposed method a real study with non-standard experimental designs is carried out. Reviewer: N.M.Zinchenko (Kyïv) Cited in 6 Documents MSC: 62K15 Factorial statistical designs 14Q99 Computational aspects in algebraic geometry Keywords:regression experiments; Groebner bases Software:CoCoA; Maple PDFBibTeX XMLCite \textit{T. Holliday} et al., Comput. Stat. 14, No. 2, 213--231 (1999; Zbl 0933.62070) Full Text: DOI References: [1] Caboara, M. & Riccomagno, E. (1997) An algebraic computational approach to the identifiability of Fourier models. Journal of Symbolic Computation (Under review). · Zbl 1130.68343 [2] Caboara, M., Pistone, G., Riccomagno, E. & Wynn, H.P. The Fan of an Experimental Design. The Annals of Statistics (Submitted). [3] Caboara, M. & Robbiano, L. (1997). Families of ideals in statistics. Proceedings of the ISSAC 97 (Maui, Hawaii, July 97) Küchlin Ed., New York, 404-117. · Zbl 0938.62080 [4] Capani, A., Niesi, G. & Robbiano, L. (1995) CoCoA, a system for doing Computations in Commutative Algebra. Available via anonymous ftp from lancelot.dima.unige.it. See also http://cocoa.dima.unige.it/. [5] Char, B., Geddes, K., Gonnet, G., Leong, B., Monogan, M & Watt, S. (1991) MAPLE V Library Reference Manual. Springer-Verlag New York. · Zbl 0763.68046 [6] Cox, D., Little, J. & O’Shea, D. (1996) Ideal, Varieties, and Algorithms, Springer-Verlag, New York. (Second edition). · Zbl 0861.13012 [7] Draper, N.T., Pozueta, L., Davis, T.P., & Grove, D.M. (1994) Isolation of degrees of freedom for Box-Behnken designs. Technometrics, Vol.36, No.3, pp.283-291. · Zbl 0925.62340 [8] Fontana, R., Pistone, G. & Rogantin, M-P. (1997). Algebraic analysis and generation of two-level designs. Statistica Applicata. 9, 1 (In press). [9] Heywood, J.B. (1988) Internal Combustion Engine Fundamentals. McGraw-Hill. [10] Holliday, T. (1996) The Design and Analysis of Engine Mapping Experiments, PhD Thesis, University of Birmingham. [11] Holliday, T., Lawrance, A.J. & Davis, T.P. (1997). Engine mapping: a two-stage regression approach. Technometrics (to appear). [12] Pistone, G. & Wynn, H.P. (1996) Generalised Confounding with Gröbner Bases, Biometrika 83, 3:653-666. · Zbl 0928.62060 [13] Sturmfels B. Gröbner Bases and Convex polytopes. Ed. AMS, Providence R I, 1995. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.