Relations among conditional probabilities
Jason Morton

TL;DR
This paper develops a mathematical framework using Groebner bases to understand relations among conditional probabilities, connecting algebraic structures to probabilistic concepts and exploring geometric representations.
Contribution
It introduces a Groebner basis for relations among conditional probabilities and links these to geometric objects like generalized permutohedra and simplexes.
Findings
Derived a Groebner basis for conditional probability relations
Connected algebraic relations to geometric structures such as permutohedra
Described a conditional probability simplex for various cases
Abstract
We describe a Groebner 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.
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Taxonomy
TopicsBayesian Modeling and Causal Inference · Polynomial and algebraic computation
