Details:
Title  Betti numbers of polynomial hierarchical models for experimental designs.  Author(s)  Hugo MaruriAguilar, Eduardo SáenzdeCabezón, Henry P. Wynn  Type  Article in Journal  Abstract  Polynomial models, in statistics, interpolation and other fields, relate an output η to a set of input variables (factors), x = (x 1,..., x d ), via a polynomial η(x 1,...,x d ). The monomials terms in η(x) are sometimes referred to as “main effect” terms such as x 1, x 2, ..., or “interactions” such as x 1 x 2, x 1 x 3, ... Two theories are related in this paper. First, when the models are hierarchical, in a welldefined sense, there is an associated monomial ideal generated by monomials not in the model. Second, the socalled “algebraic method in experimental design” generates hierarchical models which are identifiable when observations are interpolated with η(x) based at a finite set of points: the design. We study conditions under which ideals associated with hierarchical polynomial models have maximal Betti numbers in the sense of Bigatti (Commun Algebra 21(7):2317–2334, 1993). This can be achieved for certain models which also have minimal average degree in the design theory, namely “corner cut models”.  Keywords  Experimental design, Hilbert function, Gröbner fan, Betti numbers  ISSN  10122443; 15737470/e 
URL 
http://link.springer.com/article/10.1007%2Fs1047201292959 
Language  English  Journal  Ann. Math. Artif. Intell.  Volume  64  Number  4  Pages  411426  Publisher  Springer International Publishing, Cham  Year  2012  Edition  0  Translation 
No  Refereed 
No 
