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Title: Bayesian estimation of controlled branching process choice without explicit likelihood Authors:  Miguel Gonzalez Velasco - University of Extremadura (Spain)
Carmen Minuesa Abril - Autonomous University of Madrid (Spain)
Ines M del Puerto - University of Extremadura (Spain) [presenting]
Abstract: The purpose is to approximate the posterior distribution of the parameters of interest of controlled branching processes without explicit likelihood calculations nor any knowledge of the maximum number of offspring that an individual can produce. We consider that only the population sizes at every generation and at least the number of progenitors of the last generation are observed. Still, the number of offspring that every individual gives birth to is unknown at any generation. The method proposed is two-fold. We firstly make use of an Approximate Bayesian Computation based on sequential Monte Carlo (SMC ABC) model choice algorithm to estimate the posterior distribution of the maximum reproductive capacity. Secondly, to estimate the posterior distribution of the parameters of interest, we run the rejection ABC algorithm and the post-processing on the output of the previous method by considering an appropriated summary statistic. The accuracy of the proposed method is illustrated employing a simulated example developed with the statistical software R.