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Abstract:
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The use of model-assisted inference in modern science has become increasingly popular. This popularity has been motivated by the need to predict complex real-world processes in regimes where descriptive statistical models alone are insufficient. Such scenarios arise naturally in using simulation models of climate to extrapolate climate behaviour into the future, or using stochastic models to model as yet unobserved events. The computer model calibration experiment is a popular statistical framework that combines mathematical models of the process being studied with statistical techniques to leverage descriptive and theoretical information in order to improve our ability to predict the behaviour of such processes. This statistical technique treats the mathematical model as implemented on computer as an unknown but deterministic response surface. However, these mathematical models are often solutions to complex differential equation models or other stochastic models which are not deterministic. In this paper, we develop a statistical calibration approach that can incorporate such uncertainty when realizations of the simulation model are available.
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