Seth Sullivant, Department of Mathematics, University of California Berkeley
"Finiteness Theorems for Markov Bases of Hierarchical Models"
Markov bases of hierarchical models are algebraic tools for analyzing multidimensional discrete data. In particular, they are used to generate random draws from the set of all nonnegative integral multidimensional arrays with given fixed marginal totals. Recent results of De Loera and Onn, suggest that it is unlikely that there is any global characterization of Markov bases, even for three-way tables. On the other hand, Markov bases possess striking combinatorial properties which can be used to make them easier to compute. In this talk, I will describe finiteness theorems that relate Markov basis elements of large multidimensional arrays to Markov basis elements of smaller arrays.
WEDNESDAY, September 22, 2004