Graduate Computational Algebraic Geometry Seminar
Elizabeth Gross
UIC
Dynamic Markov Bases
Abstract: In this talk, we demonstrate a package for Macaulay2 that
generates Markov moves on the fly for decomposable hierarchical models.
Hypothesis testing in statistics can become problematic for large
contingency tables. In order to approximate test statistics, one can use the
Metropolis-Hastings algorithm to perform a random walk on all contingency
tables with the same sufficient sufficient statistics. A Markov basis is a
set of moves that ensures such a random walk connects every pair of tables.
In practice, a Markov basis is computed and stored before running a MCMC
algorithm such as the Metropolis-Hastings, however, since a Markov basis can
be quite large, it is desirable to be able to generate a Markov move as
needed. Such a dynamic algorithm is possible to implement with statistical
models whose Markov bases have known closed forms like decomposable
hierarchical models. This is joint work with Vishesh Karwa.
Thursday October 27, 2011 at 1:00 PM in SEO 1227