Sensitivity of some posterior summaries when the prior is unimodal with specified quantiles

Prior information is modeled either by (1) a class of unimodal distributions with specified quantiles, or by (2) an ∈-contamination class with contaminations subject to unimodal and quantile restrictions. We show how the ranges of certain posterior summaries can be found. Using numerical examples, we compare the robustness behaviour under these classes, and assess the effect, in terms of robustness, of specifying a base prior.