BAYESIAN MODELS FOR SPARSE PROBABILITY TABLES

We wish to make inferences about the conditional probabilities p(y/x), many of which are zero, when the distribution of X is unknown and one observes only a multinomial sample of the Y variates. To do this, fix ed likelihood ratio models and quasi-incremental distributions are def ined. It is shown that quasi-incremental distributions are intimately linked to decomposable graphs and that these graphs can guide us to tr ansformations of X and Y which admit a conjugate Bayesian analysis on a reparametrization of the conditional probabilities of interest.