On asymptotic posterior normality for controlled branching processes

For a controlled branching process (CBP) with offspring distribution belonging to the power series family, the asymptotic normality of the posterior distribution of the basic parameter and the offspring mean is proved. As practical applications, we calculate asymptotic high probability density credibility sets for the offspring mean and we provide a rule to make inference about the value of this parameter. Moreover, the asymptotic posterior normality of the respective parameters of two classical branching models, namely the standard Galton-Watson process and the Galton-Watson process with immigration, is derived as particular cases of the CBP.