  Recursive graphical models usually underlie the statistical modelling
concerning probabilistic expert systems based on Bayesian networks. This paper
defines a version of these models, denoted as recursive exponential models,
which have evolved by the desire to impose sophisticated domain knowledge onto
local fragments of a model. Besides the structural knowledge, as specified by a
given model, the statistical modelling may also include expert opinion about
the values of parameters in the model. It is shown how to translate imprecise
expert knowledge into approximately conjugate prior distributions. Based on
possibly incomplete data, the score and the observed information are derived
for these models. This accounts for both the traditional score and observed
information, derived as derivatives of the log-likelihood, and the posterior
score and observed information, derived as derivatives of the log-posterior
distribution. Throughout the paper the specialization into recursive graphical
models is accounted for by a simple example.
