Concentration Function in a Robust Bayesian Framework

摘要

In the robust Bayesian analysis, posterior ranges of some functions of theunknown parameters are considered when the prior distribution varies in a class Gamma. The usual functions (probability of given sets, mean, variance, etc.) are capable of describing the variation of just one aspect of the posterior distribution. The concentration function may describe more globally the variability in the posterior distribution, because it measures simultaneously the minimum posterior probability achievable by the sets with the same probability under the reference distribution. In this paper, some properties of the concentration functions are studied when some epsilon-contamination classes Gamma are considered; two well-known indices are employed as a measure of the robustness and, finally, the results are applied to some examples.