Two Polynomial Representations of Experimental Design
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In the context of algebraic statistics an experimental design is described by a set of polynomials called the design ideal. This, in turn, is generated by finite sets of polynomials. Two types of generating sets are mostly used in the literature: Gröbner bases and indicator functions. We briefly describe them both, how they are used in the analysis and planning of a design and how to switch between them. Examples include fractions of full factorial designs and designs for mixture experiments.
AMS Subject Classification62K15 13P10
KeywordsAlgebraic Statistics Factorial design Gröbner basis Indicator function Mixture design
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- Fontana, R., Pistone, G., Rogantin, M.-P., 1997. Algebraic analysis and generation of two-levels designs. Statistica Applicata, 9 (1), 15–29.Google Scholar
- Maruri-Aguilar, H., Notari, R., Riccomagno, E., 2007. On the description and identifiability analysis of mixture designs. Statistica Sinica, (1417–1440).Google Scholar
- Pistone, G., Riccomagno, E., Rogantin, M., 2007. In Search for Optimality in Design and Statistics: Algebraic and Dynamical System Methods. Ch. Methods in Algebraic Statistics for the Design of Experiments, pp. 97–132.Google Scholar
- Pistone, G., Rogantin, M., 2007 a. Algebraic statistics of level codings for fractional factorial designs. J. Statist. Plann. Inference 234–244.Google Scholar