Assessing Model Discrepancy Using a Multi-Model Ensemble

Any model-based prediction must take account of the discrepancy between the model and the underlying system. In physical systems such as climate, where a typical system component is indexed by space, time, and type, this discrepancy has a complex joint structure, which makes direct elicitation very demanding. Here we propose an alternative to direct elicitation, based on judgements about a collection of model-evaluations, known as a Multi-Model Ensemble (MME). The crucial statistical modelling framework is that of second-order exchangeability, within a Bayes linear treatment. We show how a secondorder exchangeable MME can be used to learn about the discrepancy, and also how it can be used to support our judgements about the relation between the model-evaluations and the system. We illustrate our approach with global surface temperature, using an MME constructed for the IPCC Fourth Assessment Report. ∗Corresponding author: Department of Mathematics, University Walk, Bristol, BS8 1TW, UK; email [email protected].