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Recursive graphical models usually underlie the statistical modellingconcerning probabilistic expert systems based on Bayesian networks. This paperdefines a version of these models, denoted as recursive exponential models,which have evolved by the desire to impose sophisticated domain knowledge ontolocal fragments of a model. Besides the structural knowledge, as specified by agiven model, the statistical modelling may also include expert opinion aboutthe values of parameters in the model. It is shown how to translate impreciseexpert knowledge into approximately conjugate prior distributions. Based onpossibly incomplete data, the score and the observed information are derivedfor these models. This accounts for both the traditional score and observedinformation, derived as derivatives of the log-likelihood, and the posteriorscore and observed information, derived as derivatives of the log-posteriordistribution. Throughout the paper the specialization into recursive graphicalmodels is accounted for by a simple example.

Score and Information for Recursive Exponential Models with Incomplete Data