Robust Estimation in Controlled Branching Processes: Bayesian Estimators via Disparities

Abstract

In this paper we describe Bayesian inferential methods for data modeled by controlled branching processes that account for model robustness via the use of disparities. Under regularity conditions, we establish that estimators obtained using disparity-based posterior, such as expected and maximum a posteriori estimates, are consistent and efficient under the posited model. Additionally, we establish that the estimates are robust to model misspecification and presence of outliers. To this end, we develop several fundamental ideas relating minimum disparity estimators to Bayesian estimators obtained using the disparity-based posterior, for dependent tree-structured data. We illustrate the methodology through a simulated example and apply our methods to a real data set from cell kinetics.