Maruri-Aguilar, Hugo, Notari, Roberto and Riccomagno, Eva (2006) On the description and identifiability analysis of experiments with mixtures. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers, Vol.2006).

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Abstract

Mixture designs are represented as sets of homogeneous polynomials. Techniques from computational commutative algebra are employed to deduce generalised confounding relationships on power products and to determine families of identifiable models.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Mixture distributions (Probability theory)
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2006
Volume:	Vol.2006
Number:	No.3
Number of Pages:	41
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
References:	Abbott, J., Bigatti, A., Kreuzer, M., Robbiano, L. (2000). Computing ideals of points. J. Symbolic Comput., 30, 4, 341–356. Adams, W. W., Loustaunau, P. (1994). An introduction to Gr¨obner bases, vol. 3 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI. Aitchison, J. (1986). The statistical analysis of compositional data. Monographs on Statistics and Applied Probability. Chapman & Hall, London. Babson, E., Onn, S., Thomas, R. (2003). The Hilbert zonotope and a polynomial time algorithm for universal Gr¨obner bases. Adv. in Appl. Math., 30, 3, 529–544. Bocci, C., Dalzotto, G., Notari, R., Spreafico, M. L. (2005). An iterative construction of Gorenstein ideals. Trans. Amer. Math. Soc., 357, 4, 1417–1444 (electronic). Caboara, M., Pistone, G., Riccomagno, E., Wynn, H. (1999). The fan of an experimental design. Eurandom Preprint n. 99-038. Caboara, M., Riccomagno, E. (1998). An algebraic computational approach to the identifiability of Fourier models. JSC, 26, 2, 245–260. Claringbold, P. J. (1955). Use of the simplex design in the study of joint action of related hormones. Biometrics. CoCoATeam (). CoCoA: a system for doing Computations in Commutative Algebra. Available at http://cocoa.dima.unige.it. Cornell, J. A. (2002). Experiments with mixtures. Wiley Series in Probability and Statistics. Wiley-Interscience [John Wiley & Sons], New York, third ed. Designs, models, and the analysis of mixture data. Cox, D., Little, J., O’Shea, D. (1997). Ideal, Varieties, and Algorithms. Springer-Verlag, New York. Second Edition. — (2004). Using algebraic geometry. Springer-Verlag, New York. Second Edition. Cox, D. R. (1971). A note on polynomial response functions for mixtures. Biometrika. Draper, N. R., Pukelsheim, F. (1998). Mixture models based on homogeneous polynomials. J. Statist. Plann. Inference, 71, 1-2, 303–311. Faug`ere, J. C., Gianni, P., Lazard, D., Mora, T. (1993). Efficient computation of zerodimensional Gr¨obner bases by change of ordering. J. Symbolic Comput., 16, 4, 329–344. Giglio, B., Wynn, H. P., Riccomagno, E. (2001). Gr¨obner basis methods in mixture experiments and generalisations. In Optimum design 2000 (Cardiff), vol. 51 of Nonconvex Optim. Appl., pages 33–44. Kluwer Acad. Publ., Dordrecht. Grayson, D. R., Stillman, M. E. (). Macaulay 2, a software system for research in algebraic geometry. Available at http://www.math.uiuc.edu/Macaulay2/. Greuel, G.-M., Pfister, G., Sch¨onemann, H. (2005). Singular 3.0. A Computer Algebra System for Polynomial Computations, Centre for Computer Algebra, University of Kaiserslautern. http://www.singular.uni-kl.de. Hartshorne, R. (1977). Algebraic geometry. Springer-Verlag, New York. Graduate Texts in Mathematics, No. 52. Holliday, T., Pistone, G., Riccomagno, E., Wynn, H. (1999). The application of algebraic geometry to analysis of designed experiments: A case study. Computational Statistics, 14, 2, 213–231. Kreuzer, M., Robbiano, L. (2000). Computational commutative algebra. 1. Springer-Verlag, Berlin. McConkey, B., Mezey, P., Dixon, D., Grenberg, B. (2000). Fractional simplex designs for interaction screening in complex mixtures. Biometrics, 56, 824–832. McCullagh, P., Nelder, J. A. (1989). Generalised linear model. Chapman and Hall, London. Peixoto, J. L., D´ıaz, J. (1996). On the construction of hierarchical polynomial regression models. Estad´ıstica, 48, 150-151, 175–210 (1998). Piepel, G. F., Hicks, R. D., Szychowski, J. M., Loeppky, J. L. (2002). Methods for assessing curvature and interaction in mixture experiments. Technometrics, 44, 2, 161–172. Pistone, G., Riccomagno, E., Wynn, H. P. (2000). Gr¨obner basis methods for structuring and analysing complex industrial experiments. International Journal of Reliability, Quality and Safety Engineering, 7, 4, 285–300. — (2001). Algebraic Statistics, vol. 89 of Monographs on Statistics and Applied Probability. Chapman & Hall/CRC, Boca Raton. Pistone, G., Wynn, H. P. (1996). Generalised confounding with Gr¨obner bases. Biometrika, 83, 3, 653–666. Scheff´e, H. (1958). Experiments with mixtures. J. Roy. Statist. Soc. Ser. B, 20, 344–360. — (1963). The simplex-centroid design for experiments with mixtures. J. Roy. Statist. Soc. Ser. B, 25, 235–263. Snee, R., Marquardt, D. (1976). Screening concepts and designs for experiments with mixtures. Technometrics, 18, 19–29. Waller, J. N. D. J. (1985). Additivity and interaction in three-component experiments with mixtures. Biometrika. Zhang, C. Q., Chan, L. Y., Guan, Y. N., Li, K. H., Lau, T. S. (2005). Optimal designs for an additive quadratic mixture model involving the amount of mixture. Statist. Sinica, 15, 1, 165–176.
URI:	http://wrap.warwick.ac.uk/id/eprint/35563

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