C. Minuesa Abril, M. González Velasco, I. M. del Puerto García, A. N. Vidyashankar
Bayesian inferential methods for the parameters of interest in controlled branching processes that account for model robustness through the use of disparities are studied. We consider a very general one-dimensional parametric family for the offspring distribution and assume that the sample given by the entire family tree up to some generation is observed. We introduce the D-posterior density, a modified posterior obtained by replacing the log-likelihood in Bayes’ rule with a suitably scaled disparity measure. The expectation and mode of the D-posterior density are proposed as Bayes estimators for the offspring parameter, emulating the point estimators under the squared error loss function or under 0-1 loss function, respectively, for the posterior density. We analize the consistency and efficiency of the proposed estimators under the posited model. Additionally, we show that the estimates are robust to model misspecification and presence of aberrant outliers.
Palabras clave: Branching Process, Controlled Process, Disparity Measures, Robustness, Bayesian Inference.
Programado
Procesos Estocásticos y sus aplicaciones III
12 de junio de 2025 11:30
Auditorio 2. Leandre Cristòfol