Gröbner Basis Methods in Mixture Experiments and Generalisations
The theory of mixture designs has a considerable history. We address here the important issue of the analysis of an experiment having in mind the algebraic interpretation of the structural restriction Σx i = 1. We present an approach for rewriting models for mixture experiments, based on constructing homogeneous orthogonal polynomials using Gröbner bases. Examples are given utilising the approach.
Keywordsmixture experiments Gröbner Bases orthogonal polynomials homogeneous polymomials
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- Bates, R., Giglio, B., Riccomagno, E. and Wynn, H.R (1998). Gröbner basis methods in polynomial modelling. In COMPSTAT98: Proceedings in Computational Statistics Eds. R.L. Payne and P.J. Green, pp. 179–184. Heidelberg: Physica-Verlag.Google Scholar
- Caboara, M., Pistone, G., Riccomagno, E. and Wynn, H.P. (1997). The fan of an experimental design. SCU Report Number 10, University of Warwick.Google Scholar
- Cox, D., Little, J. and O’Shea, J. (1997). Ideals, Varieties and Algorithms, 2nd Edn. New York: Springer-Verlag.Google Scholar
- Giglio, B., Riccomagno, E. and Wynn, H.P. (2000). Gröbner basis strategies in regression. Applied Statistics (to appear).Google Scholar
- Holliday, T., Pistone, G., Riccomagno, E. and Wynn, H.P. (1999). The application of computational geometry to the design and analysis of experiments: a case study. Computational Statistics (in press).Google Scholar
- Riccomagno, E. (1997). Algebraic Identifiability in Experimental Design and Related Ttopics. PhD thesis, University of Warwick.Google Scholar
- Riccomagno, E., Pistone, G. and Wynn, H.P. (1998). Gröbner bases and factorisation in discrete probability and Bayes. Statistics and Computing (in press). (Special issue for the workshop “Statistics and Computing”, Montreal, 1998).Google Scholar
- Riccomagno, E., Pistone, G. and Wynn, H.P. (1999). Polynomial encoding of discrete probability. ISI Helsinki, 1999 Abstract. Submitted to Int. Stat. Review.Google Scholar
- Riccomagno, E. and Wynn, H.P. (2000). Gröbner bases, ideals and a generalised divided difference formula. Num. Math. (submitted).Google Scholar
- L. Robbiano (1998). Gröbner bases and Statistics In Proceedings of the International Conference “33 years of Gröbner Bases”. Cambridge University Press, London Mathematical Society Lecture Notes (in press).Google Scholar