Abstract

Large complex data sets typically demand approximate models at some level of specification. In such situations it is important for the analyst to examine the robustness of conclusions to approximate predictions. Recent developments in optimal control and econometrics have established formal methods for linear quadratic state space models (see e.g. Hansen and Sargent 2008) by considering the local-minimax outcome within an information divergence (Kullback-Leibler) neighbourhood around the approximating model. Here we show how these approaches can be extended to arbitrary probability models using Monte Carlo methods. We derive theoretical results establishing the uniqueness of the Kullback-Leibler criteria, as well as Bayesian non-parametric methods to sample from the space of probability distributions within a fixed divergence constraint.