After this discussion, I pointed Ryan Giordano, Tamara Broderick, and Michael Jordan to Figure 4 of this paper with Bois and Jiang as an example of “static sensitivity analysis.” I’ve never really followed up on this idea but I think it could be useful for many problems.

Giordano replied:

Here’s a copy of Basu’s robustness paper, contemporaneous with your 1996 paper, which we talked about. I think it’s a nice, easy-to-understand way to get at what you were also aiming for. In the spirit of your diagnostic graphs, I think a better use of the idea is to report a bunch of “slopes” rather than just look for the worst-case direction (there’s no reason to think the unit ball means anything when you’re comparing a large number of different prior parameters), but the basic idea of replacing derivatives with covariances seems like a good one to me.

I like this and I’d like to incorporate it into our statistical workflow.

**P.S.** The “static” in static sensitivity analysis refers to the idea that we’re doing the computations using the results of a single fitted model, rather than performing sensitivity analysis by re-fitting the model several times under different assumptions.