Relations among conditional probabilities

Authors:
Jason Morton
Affiliations:
Department of Mathematics and Statistics, McAllister Building, The Pennsylvania State University, University Park, PA 16802, United States
Venue:
Journal of Symbolic Computation
Year:
2013

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Abstract

We describe a universal Grobner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generalized permutohedra and describe a ''conditional probability simplex'' which is the image of a multigraded moment map.