Bayesian non-parametric estimation for age-dependent branching processes

The purpose of this paper is to obtain Bayes estimators for both the offspring and life-length distribution in the context of a Bellman-Harris age-dependent branching process. We take a non-parametric approach by letting the prior random distributions, for the offspring and life-length distributions, be independent Dirichlet processes. Our primary results concern the derivation of Bayes estimators, under weighted squared error loss for each distribution. We also indicate some of their asymptotic properties and briefly discuss the modifications that become necessary when the initial information is such that the prior random distribution cannot be taken to be independent.