Quantifier Elimination for Statistical Problems

01/23/2013

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by   Dan Geiger, et al.

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Recent improvement on Tarski's procedure for quantifier elimination in the first order theory of real numbers makes it feasible to solve small instances of the following problems completely automatically: 1. listing all equality and inequality constraints implied by a graphical model with hidden variables. 2. Comparing graphyical models with hidden variables (i.e., model equivalence, inclusion, and overlap). 3. Answering questions about the identification of a model or portion of a model, and about bounds on quantities derived from a model. 4. Determing whether a given set of independence assertions. We discuss the foundation of quantifier elimination and demonstrate its application to these problems.