Support Sets in Exponential Families and Oriented Matroid Theory

Details Support Sets in Exponential Families and Oriented Matroid Theory Support Sets in Exponential Families and Oriented Matroid Theory

2009-06-30

arxiv.org/abs/0906.5462v2

International Journal of Approximate Reasoning Volume 52, Issue 5, July 2011, Pages 613-626

Mathematics

Statistics Theory

27 pages, extended version published in IJAR

Scientific paper

10.1016/j.ijar.2011.01.013

The closure of a discrete exponential family is described by a finite set of equations corresponding to the circuits of an underlying oriented matroid. These equations are similar to the equations used in algebraic statistics, although they need not be polynomial in the general case. This description allows for a combinatorial study of the possible support sets in the closure of an exponential family. If two exponential families induce the same oriented matroid, then their closures have the same support sets. Furthermore, the positive cocircuits give a parameterization of the closure of the exponential family.

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