Estimating the parameters of mixed Bayesian networks from incomplete data

Under complete data, there are closed-form maximum likelihood estimators for mixed Bayesian networks composed of discrete models, conditional Gaussian models and conditional Gaussian regression models. We describe an extension to Lauritzen´ expectation-maximisation algorithm, which estimates the parameters of discrete networks from incomplete data, to the more general case of mixed continuous and discrete variable networks. A simple mixed network that is easy to manipulate is the leaf node continuous Bayesian network (LNCBN). Fast algorithms for estimation and marginalisation of LNCBNs are described