Optimal selection from distributions with unknown parameters: Robustness on Bayesian models

The paper considers the problem of making one choice from a known number of i.i.d. alternatives. It is assumed that the distribution of the alternatives has some unknown parameter. It follows a Bayesian approach to maximize the discounted expected value of the chosen alternative minus the costs for the observations. For the case of gamma and normal distribution the paper investigates the sensitivity of the solution with respect to the prior distributions. The present main objective is to derive monotonicity and continuity results for the dependence on parameters of the prior distributions. Thus the paper proves some sort of Bayesian robustness of the model.