Approximate Models and Robust Decisions

Statistical decisions based partly or solely on predictions from probabilistic models may be sensitive to model misspecification. Statisticians are taught from an early stage that “all models are wrong ” but little formal guidance exists on how to assess the impact of model approximation, or how to proceed when optimal actions appear sensitive to model fidelity. This article presents one potential applied framework to address this. We discuss diagnostic techniques, including graphical approaches and summary statistics, to help highlight deci-sions made through minimised expected loss that are sensitive to model misspecification. We then derive formal methods for decision making under model misspecification by quan-tifying stability of optimal actions to perturbations within a neighbourhood of model space, defined via an information (Kullback-Leibler) divergence around the approximating model. This latter approach draws heavily from recent work in the robust control, macroeconomics and financial mathematics literature. We adopt a Bayesian approach throughout although the methods are agnostic to this position