Galton-Watson process: a non parametric prior for the offspring distribution

In this article we propose a non parametric prior for the probabilities of the Galton- Watson process based on the Dirichlet Process. After recalling the main properties of the Galton-Watson process and presenting the estimation methods already present in the lit- erature, such as maximum likelihood and Bayesian conjugate analysis, we define the new prior by pointing out how it is more general than the Dirichlet prior used in the conjugate analysis, which is a special case of our extension. Finally, we show the results of a simula- tion study illustrating how our analysis leads to a more accurate classification of the process.