Risk, Ambiguity, and Misspecification: Decision Theory, Robust Control, and Statistics

We connect variational preferences with the likelihood functions and prior probabilities over parameters that are building blocks of statistics and econometrics. We use relative entropy and other statistical divergences as cost functions in the variational preferences of someone who is ambiguous in the sense of not having a unique prior over a discrete set or manifold of statistical models (i.e., likelihood functions) and who suspects that each statistical model is misspecified. We connect variational preferences to theories of robust control and statistical approximation.