Given a multinomial decomposable graphical model, we identify several alternative parametrizations; in particular we consider conditional probabilities of clique-residuals given separators, as well as generalized log-odds-ratios. For each such parametrization, we construct the corresponding...

Reference analysis is one of the most successful general methods to derive noninformative prior distributions. In practice, however, reference priors are often difficult to obtain. Recently developed theory for conditionally reducible natural exponential families identifies an attractive...