Title: Controlled branching processes: Estimation based on ABC-SMC methodology
Authors: Miguel Gonzalez Velasco - University of Extremadura (Spain) [presenting]
Carmen Minuesa Abril - University of Extremadura (Spain)
Ines M del Puerto - University of Extremadura (Spain)
Abstract: The focus is on the estimation of the posterior distribution of the main parameters of a controlled branching process (CBP) without explicit likelihood calculations. Specifically, we focus on the case where we have no prior knowledge of the maximum number of offspring that an individual can produce. Our approach has two steps. In the first stage, we estimate the posterior distribution of the maximum progeny per individual using an approximate Bayesian computation (ABC) algorithm for model choice with the raw data and based on sequential importance sampling. In the second step, using the values simulated in the previous stage, we estimate the posterior distribution of the main parameters of a CBP by applying the rejection ABC algorithm with an appropriate summary statistic and a post-processing adjustment. We show the accuracy of the proposed methodology via simulated examples and via real data from models that incorporate a carrying capacity, in both cases making use of the statistical software R.