Decision-theoretic estimation of the offspring mean in mortal branching processes

The aim of the present paper is to obtain Bayes estimators for the offspring mean of a simple branching process with a power series offspring probability distribution. We study the sensitivity behavior of the obtained estimators with respect to the choice of the loss function. We propose a minimax criterion using the Bayes risk for ranking the effectiveness (in the sense of robustness) of the loss functions that are being used. In particular, we show analytically that the Bayes estimator under the relative squared-error loss is preferable to the posterior mean. The usefulness of the analytical results is illustrated on some actual epidemic data from smallpox outbreaks.