Let X and Y be random variables. Quasi-independence models are log-linear models that describe a situation in which some states of X and Y cannot occur together, but X and Y are otherwise independent. We characterize which quasi-independence models have rational maximum likelihood estimator, or MLE, based on combinatorial features of the bipartite graph associated to the model. In this case, we give an explicit formula for the maximum likelihood estimate. We also show that if a log-linear model has rational MLE, then so do all of its facial submodels.

Organizer: Ashley Tharp