  For a given discrete decomposable graphical model, we identify several
alternative parametrizations, and construct the corresponding reference priors
for suitable groupings of the parameters. Specifically, assuming that the
cliques of the graph are arranged in a perfect order, the parameters we
consider are conditional probabilities of clique-residuals given separators, as
well as generalized log-odds-ratios. We also consider a parametrization
associated to a collection of variables representing a cut for the statistical
model. The reference priors we obtain do not depend on the order of the
groupings, belong to a conjugate family, and are proper.
