Basu (1994) and Basu and DasGupta (1995) described the use of distribution bands (bounds on cumulative distribution functions) in robust Bayes analysis. Their conception seems to be limited to characterizing the robustness of the output of an analysis due to uncertainty about the proper choice of the prior distribution. Basu and DasGupta (1995) describe how to compute posterior quantiles when the prior cumulative distribution of a one-dimensional parameter q is constrained by a specified distribution band. Basu (1994) gives a general method for finding the extremum of a posterior expectation of a function of the parameter assuming the prior is symmetric and unimodal and varies within some distribution band. We would like to implement their methods, replicate their numerical examples, and possibly extend their methods for our problems. In particular, we’d like to extend the methods to handle interval data (which would represent a class of likelihoods). We would like to compute not just bounds on the expectation of the posterior, but the bounds on the entire posterior.