Details:
Title  Methods in algebraic statistics for the design of experiments.  Author(s)  G. Postone, Eva Riccomagno, M.P. Rogantin  Type  Book, Chapter in Book, Conference Proceeding  Abstract  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.  ISBN  9780387799353/hbk 
URL 
http://link.springer.com/chapter/10.1007%2F9780387799360_5 
Language  English  Pages  97132  Publisher  New York, NY: Springer  Year  2009  Edition  0  Translation 
No  Refereed 
No 
