A Class of Conjugate Hierarchical Priors for Gammoid Likelihoods

The class of gamma distributions is known to be the natural conjugate family of priors for gammoid likelihoods like e.g. the Poisson or exponential. This result is extended to the hierarchical case where the observations are stratified in a nested pattern. A suitable class of priors is a hierarchical system of finite gamma mixtures with fixed scale parameters and random shape parameters. Algorithms for posterior calculations are worked out for the two-stage hierarchy with simple gamma priors.