Support Sets in Exponential Families and Oriented Matroid Theory
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 June 2009
 arXiv:
 arXiv:0906.5462
 Bibcode:
 2009arXiv0906.5462R
 Keywords:

 Mathematics  Statistics Theory;
 52C40;
 62B05;
 14P15
 EPrint:
 27 pages, extended version published in IJAR