The challenge of understanding complex systems often gives rise to a multiplicity of models. It is natural to consider whether the outputs of these models can be combined to produce a system prediction that is more informative than the output of any one of the models taken in isolation. And, in particular, to consider the relationship between the spread of model outputs and system uncertainty. We describe a statistical framework for such a combination, based on the exchangeability of the models, and their co-exchangeability with the system. We demonstrate the simplest implementation of our framework in the context of climate prediction. Throughout we work entirely in means and variances, to avoid the necessity of specifying higher-order quantities for which we often lack well-founded judgements.
Rougier, J. C., Goldstein, M., & House, L. (2013). Second-Order Exchangeability Analysis for Multimodel Ensembles. Journal of the American Statistical Association, 108(503), 852-863. https://doi.org/10.1080/01621459.2013.802963