The Geometry of Statistical Models for Two-Way Contingency Tables with Fixed Odds Ratios

We study the geometric structure of the statistical models for two-by-two contingency tables. One or two odds ratios are fixed and the corresponding models are shown to be a portion of a ruled quadratic surface or a segment. Some pointers to the general case of two-way contingency tables are also given and an application to case-control studies is presented.Comment: References were not displaying properly in the previous versio

Star configuration points and plane curves

2siLet ℓ1,...,ℓ1 be l lines in ℙ2 such that no three lines meet in a point. Let X(l) be the set of points {ℓi ∩ ℓj {divides} 1 ≤ i < j ≤ l} ⊆ ℙ2. We call X(l) a star configuration. We describe all pairs (d, l) such that the generic degree d curve in ℙ2 contains an X(l). Our proof strategy uses both a theoretical and an explicit algorithmic approach. We also describe how one may extend our algorithmic approach to similar problems. © 2011 American Mathematical Society.openopenCarlini E.; van Tuyl A.Carlini, E.; van Tuyl, A

Special apolar subset: the case of star configurations

In this paper we consider a generic degree $d$ form $F$ in $n+1$ variables. In particular, we investigate the existence of star configurations apolar to $F$, that is the existence of apolar sets of points obtained by the $n$-wise intersection of $r$ general hyperplanes of $\mathbb{P}^n$. We present a complete answer for all values of $(d,r,n)$ except for $(d,d+1,2)$ when we present an algorithmic approach

Star configuration points and generic plane curves

Consider l lines in P^2 such that no three lines meet in a point. Let X(l) denote all points of intersections of these l lines. We describe all pairs (d,l) such that generic degree d curve in P^2 contains a X(l).Comment: 12 page

Geometry of diagonal-effect models for contingency tables

In this work we study several types of diagonal-effect models for two-way contingency tables in the framework of Algebraic Statistics. We use both toric models and mixture models to encode the different behavior of the diagonal cells. We compute the invariants of these models and we explore their geometrical structure.Comment: 20 page