  In this paper we present decomposable priors, a family of priors over
structure and parameters of tree belief nets for which Bayesian learning with
complete observations is tractable, in the sense that the posterior is also
decomposable and can be completely determined analytically in polynomial time.
This follows from two main results: First, we show that factored distributions
over spanning trees in a graph can be integrated in closed form. Second, we
examine priors over tree parameters and show that a set of assumptions similar
to (Heckerman and al. 1995) constrain the tree parameter priors to be a
compactly parameterized product of Dirichlet distributions. Beside allowing for
exact Bayesian learning, these results permit us to formulate a new class of
tractable latent variable models in which the likelihood of a data point is
computed through an ensemble average over tree structures.
