Matroids and statistical dependency

What does it mean for a set of more than two variables to be statistically dependent, even if no two of them are pairwise dependent?  We show how to measure this dependence using joint cumulants, a common statistical tool with a nice combinatorial description.  We then show that, if we make a common statistical assumption (multivariate total positivity of order 2) on data, then the resulting structure of dependencies may be described by a matroid.  We use real examples from biology to demonstrate how the description with matroids helps simplify the presentation of complex variable dependency.

I will assume no knowledge of matroids, or of statistics.  This is joint work with Amy Wagler.