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Title: Likelihood-free simulation methodologies for controlled branching processes Authors:  Miguel Gonzalez Velasco - University of Extremadura (Spain)
Carmen Minuesa Abril - University of Extremadura (Spain)
Ines M del Puerto - University of Extremadura (Spain) [presenting]
Abstract: Controlled branching processes (CBPs) are a family of discrete-time stochastic processes which are appropriate to describe population dynamics. This model generalizes the standard branching process - the so-called Galton-Watson process. As in this latter process, each individual reproduces independently of the others and following the same distribution, referred as the offspring law. The novelty of the CBP lies in the presence of a mechanism establishing the number of individuals with reproductive capacity (progenitors) in each generation. Thus, the evolution of populations suffering from the existence of predators, populations of invasive species or different migratory movements can be modelled by using this branching process. The behaviour of these processes are determined by the parameters of the model associated with the offspring and control laws and in real situations those values are unknown. The purpose is to examine likelihood-free simulation methodologies to obtain Bayesian inference for the main parameters of interest. These methodologies enable to approximate the posterior distribution of the parameters of interest satisfactorily without explicit likelihood calculations. In particular, we examine sequential Monte Carlo methods.