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Reified Bayesian Modelling and Inference for Physical Systems

by Michael Goldstein and Jonathan Rougier

We describe an approach, termed reified analysis, for linking the behaviour of mathematical models with inferences about the physical systems which the models represent. We describe the logical basis for the approach, based on coherent assessment of the implications of deficiencies in the mathematical model. We show how the statistical analysis may be carried out by specifying stochastic relationships between the model that we have, improved versions of the model that we might construct, and the system itself. We illustrate our approach with an example concerning the potential shut-down of the Thermohaline Circulation in the Atlantic Ocean.

Key words: Computer Simulator, Emulator, Model Inadequacy, Structural Error, Thermohaline Circulation (THC), Model Design

Full text of the paper (pdf), to appear in the Journal of Statistical Planning and Inference.