# Bayes Linear Emulation, History Matching, and Forecasting for Complex Computer Simulators

## Abstract

Computer simulators are a useful tool for understanding complicated systems. However, any inferences made from them should recognize the inherent limitations and approximations in the simulator’s predictions for reality, the data used to run and calibrate the simulator, and the lack of knowledge about the best inputs to use for the simulator. This article describes the methods of emulation and history matching, where fast statistical approximations to the computer simulator (emulators) are constructed and used to reject implausible choices of input (history matching). Also described is a simple and tractable approach to estimating the discrepancy between simulator and reality induced by certain intrinsic limitations and uncertainties in the simulator and input data. Finally, a method for forecasting based on this approach is presented. The analysis is based on the Bayes linear approach to uncertainty quantification, which is similar in spirit to the standard Bayesian approach but takes expectation, rather than probability, as the primitive for the theory, with consequent simplifications in the prior uncertainty specification and analysis.

## Keywords

Computer simulators Bayes linear Emulation Model discrepancy History matching Calibration Internal discrepancy Forecasting## References

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