Bayesian consistency, or (again) lack thereof
In applied math, the model is almost always mis-specified, and so we have to ask “if the truth is complicated and I apply Bayesian procedures to my simplified model, what kind of mistakes am I likely (or not likely) to make?”
Wilks’ phenomenon, or lack thereof
I commonly find myself in a situation where I want to decide whether or not a certain mechanism is present in an applied problem.