Markov bases for decomposable graphical models

Abstract

We show that primitive data swaps or moves are the only moves that have to be included in a Markov basis that links all the contingency tables having a set of fixed marginals when this set of marginals induces a decomposable independence graph. We give formulae that fully identify such Markov bases and show how to use these formulae to dynamically generate random moves. © 2003 ISI/BS.