Non-parametric Bayesian estimation for multitype branching processes through simulation-based methods

The problem of statistical inference from a Bayesian outlook is studied for the multitype Galton–Watson branching process, considering a non-parametric framework. The only data assumed to be available are each generation's population size vectors. The Gibbs sampler is used in estimating the posterior distributions of the main parameters of the model, and the predictive distributions for as yet unobserved generations. The algorithm provided is independent of whether the process becomes extinct or not. The method is illustrated with simulated examples.