Bayesian estimators of the Gamma distribution
  In this paper we introduce two Bayesian estimators for learning the parameters of the Gamma distribution. The first algorithm uses a well known unnormalized conjugate prior for the Gamma shape and the second one uses a non-linear approximation to the likelihood and a prior on the shape that is conjugate to the approximated likelihood. In both cases use the Laplace approximation to compute the required expectations. We perform a theoretical comparison between maximum like- lihood and the presented Bayesian algorithms that allow us to provide non-informative parameter values for the priors hyper parameters. We also provide a numerical comparison using synthetic data. The introduction of these novel Bayesian estimators open the possibility of including Gamma distributions into more complex Bayesian structures, e.g. variational Bayesian mixture models. 
A. Llera and C. F. Beckmann
stat.ME