Context Speciic Interaction Models

Interaction models for categorical data play a central role in applied statistics. In particular, decomposable models have obtained a dominant position as the basis for structural learning and the development of eecient computational algorithms in connection with Bayesian networks for decision support. The present paper generalizes decompos-able models to cover log linear models, where interactions may be present only in speciic contexts (CSI-models). It is shown that the model function of a decomposable CSI-model has a factorization in terms of marginals. It is illustrated that this provides a much richer class of operational models, which must be expected to be the starting point for the development of a new generation of eeective computational algorithms for decision support systems based on Bayesian networks with context speciic independencies.