A1577
Title: On Bayesian estimation via divergences for controlled branching processes
Authors: Ines M del Puerto - University of Extremadura (Spain) [presenting]
Miguel Gonzalez Velasco - University of Extremadura (Spain)
Anand Vidyashankar - George Mason University (United States)
Carmen Minuesa - University of Extremadura (Spain)
Abstract: The focus is on Bayesian inferential methods for the parameters of interest in controlled branching processes that account for model robustness through the use of disparities. The offspring distribution is assumed to belong to a very general one-dimensional parametric family, and the sample given by the entire family tree up to some generation is observed. In this setting, the D-posterior density is defined, a density function which is obtained by replacing the log-likelihood in the Bayes rule with a conveniently scaled disparity measure. The expectation and mode of the D-posterior density, denoted as EDAP and MDAP estimators, respectively, 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. Under regularity conditions, the established EDAP and MDAP estimators are consistent and efficient under the posited model. Additionally, it is shown that the estimates are robust to model misspecification and the presence of aberrant outliers. To this end, several fundamental ideas are developed, relating minimum disparity estimators to Bayesian estimators built on the disparity-based posterior, for dependent tree-structured data.
