Developing models to describe real systems is a challenge because it is difficult to assess and control the residual between the two entities. Bayesian updating of a belief about model accuracy across an ensemble of available models can lead to spurious results, since the application of Bayes' rule presupposes that an accurate model is contained in the ensemble with certainty. We present a framework in which this assumption can be dropped. The basic idea is to extend Bayes' rule to the exhaustive, but unknown space of all models, and then contract it again to the known set of models by making best/worst case assumptions for the remaining space. We show that this approach leads to an epsilon-contamination model for the posterior belief, where the epsilon-contamination is updated along with the distribution of belief across available models. In essence, the epsilon-contamination provides an additional test on the accuracy of the overall model ensemble compared to the data, and will grow rapidly if the ensemble fails such a test. We demonstrate our concept with an example of autoregressive processes.
Keywords. Bayesian updating, prediction, model accuracy, epsilon-contamination model, AR process
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Department of Engineering and Public Policy
Carnegie Mellon University
Pittsburgh, PA 15213