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Title: Bayesian inference in two-sex branching processes with mutations: ABC approach Authors:  Cristina Gutierrez Perez - University of Extremadura (Spain) [presenting]
Miguel Gonzalez Velasco - University of Extremadura (Spain)
Rodrigo Martinez Quintana - University of Extremadura (Spain)
Abstract: A two-sex two-type branching process was recently introduced to analyze the evolution of the numbers of alleles and their mutations of a Y-linked gene. Since genes associated to the Y-chromosome, as well as mutation in there, are of special interest due to their direct relation with male fertility problems or the history of paternal lineages, the interest of how the number of carriers of these genes evolve in a population makes necessary to solve the problem of estimating the main parameters of this model.To this aim, the Approximate Bayesian Computation (ABC) methodology is developed to approximate the posterior distributions of the parameters of such model. For that, it is considered a realistic sampling scheme where the total numbers of females and males (with unrecognized genotypes) are observed in each generation up to determined one. Moreover, from the last generation, the information of the total number of males of different genotypes and those which are mutants among them is added. Finally the accuracy of the procedure using a simulated study is illustrated.