Dipartimento di Scienze Statistiche

In the presence of prior information on an unknown parameter of a statistical model, Bayesian and frequentist estimates based on the same observed data do not coincide. However, in many standard parametric problems, their discrepancy tends to be reduced as the sample size increases. In this paper we consider the pre-experimental design problem of selecting sample sizes that guarantee large probabilities of observing a small discrepancy between Bayesian and frequentist point estimates of a parameter. We propose a Bayesian predictive approach and we illustrate some examples using the normal model. We argue that these examples may be discussed even in introductory-level courses in Bayesian inference.