### The algebraic method in statistics: Betti numbers and Alexander duality

**Wynn, H **

Friday 02 September 2011, 11:00-11:30

Seminar Room 1, Newton Institute

#### Abstract

After a brief review of the algebraic method in statistics, using G-bases, some newer results are described. The first relates the average degree concept to the Betti numbers of the monomial ideal of models. "Flatter" models in the sense of having lower degree are associated with more complex ideals having larger Betti numbers. The Alexander duality relates models and their complements within a factorial framework and leads to large classes of design for which it is straightforward to read off the model structure.

#### Presentation

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