Abstract
In this paper we demonstrate how Gr�bner bases and other algebraic
techniques can be used to explore the geometry of the probability
space of Bayesian networks with hidden variables. These techniques
employ a parametrisation of Bayesian network by moments rather than
conditional probabilities. We show that whilst Gr�bner bases help
to explain the local geometry of these spaces a complimentary analysis,
modelling the positivity of probabilities, enhances and completes
the geometrical picture. We report some recent geometrical results
in this area and discuss a possible general methodology for the analyses
of such problems.
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