A likelihood based robust Bayesian summary

In a global Bayesian robustness study, one finds the range of a posterior quantity of interest over a class of plausible priors. However, not all the values in the range would be equally supported by the data. In evaluating robustness, it would be of interest to assess the amount of "data support" for each value in the range. The values that have relatively little data support may be ruled out effectively reducing the range. Here, we propose a likelihood based robustness summary, which includes a measure of data support along with the range, that may be useful in better assessing the robustness. In most cases, this summary can be obtained without any additional computation.