Title: Inference based on approximate Bayesian computation methods for X-linked two-sex branching processes
Authors: Miguel Gonzalez Velasco - University of Extremadura (Spain) [presenting]
Cristina Gutierrez Perez - University of Extremadura (Spain)
Alicia Leon Naranjo - Universidad de Extremadura (Spain)
Rodrigo Martinez Quintana - University of Extremadura (Spain)
Abstract: The evolution of the number of individuals carrying the alleles, $R$ and $r$, of a gene linked to $X$ chromosome has been described using a multitype two-sex branching process. The $R$ allele is considered dominant, and the $r$ allele is supposed to be recessive and defective, responsible for a disorder. Hemophilia, red-green color blindness or the Duchenne and Becker's muscular dystrophies are examples of this kind of diseases. For this model, we investigate the estimation of its main parameters from a Bayesian standpoint. Concretely, we apply the Approximate Bayesian Computation (ABC) methodology to approximate its posterior distributions. The accuracy of the procedure is illustrated and discussed by way of a simulated example developed with R.