  When the historical data are limited, the conditional probabilities
associated with the nodes of Bayesian networks are uncertain and can be
empirically estimated. Second order estimation methods provide a framework for
both estimating the probabilities and quantifying the uncertainty in these
estimates. We refer to these cases as uncer tain or second-order Bayesian
networks. When such data are complete, i.e., all variable values are observed
for each instantiation, the conditional probabilities are known to be
Dirichlet-distributed. This paper improves the current state-of-the-art
approaches for handling uncertain Bayesian networks by enabling them to learn
distributions for their parameters, i.e., conditional probabilities, with
incomplete data. We extensively evaluate various methods to learn the posterior
of the parameters through the desired and empirically derived strength of
confidence bounds for various queries.
