Mixtures of experts for understanding model discrepancy in dynamic computer models

There are many areas of science and engineering where research and decision making are performed using computer models. These computer models are usually deterministic and may take minutes, hours or days to produce an output for a single value of the model inputs. Fitting mixtures of experts of computer models where the expert components use different values of the computer model parameters is considered. The efficient calibration of such models using emulators, which are fast statistical surrogates for the computer model, is discussed. It is argued that mixtures of experts are often insightful for describing model discrepancy and ways in which the computer model can be improved. This is not a strength of standard approaches to the statistical analysis of computer models where a certain “best input” assumption is usually made and model discrepancy is often described through a stationary Gaussian process prior on the discrepancy function. Application of the framework is presented for a dynamic hydrological rainfall-runoff model in which the mixture approach is helpful for highlighting model deficiencies.