Robustifying the little Bayesian updating problem

We want to robustify the solution to Need 6 (Solve a little Bayesian updating problem). That is, we want to find the class of posteriors that would result from using Bayes’ rule to combine the likelihood function with all possible prior distributions that would be consistent with the information

W

[23, 33],

H

[112, 150], and

A

[2000, 3200].

This set of priors would include any prior whose support is entirely within this box in w,h,a-space, including extreme cases such as all the degenerate priors whose supports are single points in that space, two points, etc. We are interested in the credal set of resulting posterior distributions. We expect the smallest possible p-boxes that enclose the marginal posterior CDFs for the three random variables will be equivalent to the intervals

W = [23, 28.57],

H = [112, 139.13],

A = [2576, 3200].