Quantifier Elimination for Statistical Problems
This work addresses challenges in statistical inference for researchers dealing with graphical models, though it is incremental as it builds on existing quantifier elimination methods.
The paper tackles the problem of solving statistical problems like listing constraints, comparing models, and answering identification questions in graphical models with hidden variables, by applying an improved quantifier elimination procedure to automatically handle small instances.
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.