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Methods in Algebraic Statistics for the Design of Experiments

  • G. Pistone
  • E. Riccomagno
  • M. P. Rogantin
Part of the Springer Optimization and Its Applications book series (SOIA, volume 28)

Summary

We present a brief review of classical experimental design in the spirit of algebraic statistics. Notion of identifiability, aliasing and estimability of linear parametric functions, confounding are expressed in relation to a set of polynomials identified by the design, called the design ideal. An effort has been made to indicate the classical linear algebra counterpart of the objects of interest in the polynomial space, and to indicate how the algebraic statistics approach generalizes the classical theory. In the second part of this chapter we address new questions: a seemingly limitation of the algebraic approach is discussed and resolved in the ideas of minimal and maximal fan designs, again generalizing classical notions; an algorithm is provided to switch between two major representations of a design, one of which uses Gröbner bases and the other one uses indicator functions. Finally, all the theory in the chapter is applied and extended to the class of mixture designs which present a challenging structure and questions.

Keywords

Indicator Function Orthogonal Array Full Factorial Design Fractional Factorial Design Counting Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media LLC 2009

Authors and Affiliations

  1. 1. Department of Mathematics, Politecnico di Torino Torino Italy
  2. 2. Dipartimento di Matematica, Universit`a degli Studi di Genova Genova Italia
  3. 3.Cardiff Dipartimento di Matematica, Universit`a degli Studi di Genova GenovaItalia

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