A class of flat prior distributions for the Poisson-gamma hierarchical model

Fernando O. Schmitt, Gustavo L. Gilardoni, J. A. A. Andrade

Statistica Neerlandica 73 (2019) 414-433

https://doi.org/10.1111/stan.12176

A wide class of prior distributions for the Poisson‐gamma hierarchical model is proposed. Prior distributions in this class carry vague information in the sense that their tails exhibit slow decay. Conditions for the propriety of the resulting posterior density are determined, as well as for the existence of posterior moments of the Poisson rate of either an observed or an unobserved unit.