  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.
