  Dealing with uncertainty in Bayesian Network structures using maximum a
posteriori (MAP) estimation or Bayesian Model Averaging (BMA) is often
intractable due to the superexponential number of possible directed, acyclic
graphs. When the prior is decomposable, two classes of graphs where efficient
learning can take place are tree structures, and fixed-orderings with limited
in-degree. We show how MAP estimates and BMA for selectively conditioned
forests (SCF), a combination of these two classes, can be computed efficiently
for ordered sets of variables. We apply SCFs to temporal data to learn Dynamic
Bayesian Networks having an intra-timestep forest and inter-timestep limited
in-degree structure, improving model accuracy over DBNs without the combination
of structures. We also apply SCFs to Bayes Net classification to learn
selective forest augmented Naive Bayes classifiers. We argue that the built-in
feature selection of selective augmented Bayes classifiers makes them
preferable to similar non-selective classifiers based on empirical evidence.
