Robust Estimation In Controlled Branching Processes: Bayesian Estimators Via Disparities*

In this paper we describe Bayesian inferential methods for data mod-eled by controlled branching processes that account for model robustness via the use of disparities. Under regularity conditions, we establish that estimators ob-tained 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 dis-parity estimators to Bayesian estimators obtained using the disparity-based pos-terior, 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.