  Bayesian networks are graphical models to represent the probabilistic
relationships between variables in the Bayesian framework. The knowledge of all
variables can be updated using new information about some of the variables. We
show that relying on the Bayesian network interpretation enables large scale
inference and gives flexibility in incorporating prior assumptions and
constraints into the nuclear data evaluation process, such as sum rules and the
non-negativity of cross sections. The latter constraint is accounted for by a
non-linear transformation and therefore we also discuss inference in Bayesian
networks with non-linear relationships. Using Bayesian networks, the evaluation
process yields detailed information, such as posterior estimates and
uncertainties of all statistical and systematic errors. We also elaborate on a
sparse Gaussian process construction compatible with the Bayesian network
framework that can for instance be used as prior on energy-dependent model
parameters, model deficiencies and energy-dependent systematic errors of
experiments. We present three proof-of-concept examples that emerged in the
context of the neutron data standards project and in the ongoing international
evaluation efforts of $^{56}$Fe. In the first example we demonstrate the
modelization and explicit estimation of relative energy-dependent error
components of experimental datasets. Then we show an example evaluation using
the outlined Gaussian process construction in an evaluation of $^{56}$Fe in the
energy range between one and two MeV, where R-Matrix and nuclear model fits are
difficult. Finally, we present a model-based evaluation of $^{56}$Fe between 5
MeV and 30 MeV with a sound treatment of model deficiencies. The R scripts to
reproduce the Bayesian network examples and the nucdataBaynet package for
Bayesian network modeling and inference have been made publicly available.
