Resumen de Parametric bayesian estimation for branching processes with immigration through MCMC methods
Branching processes with immigration are well-known stochastic models which describe the evolution along generations of populations where immigration of individuals from an outer source is allowed. The behaviour of these populations it is strongly related to the magnitude of the offspring mean. In practice this value is usually unknown and its estimation is necessary. In this work, we deal with the problem of estimating the offspring mean assuming that the only observable data are the total number of individuals in each generation and, therefore, considering that the number of immigrants is not available. We set out the problem from a Bayesian outlook, assuming offspring and immigration distributions belonging to the power series family.We provide an algorithm, based on the Gibbs sampler, to approach the posterior distribution of the offspring mean. Finally, we show the accuracy of this algorithm by way of several examples.
