Bayesian emulation of complex multi-output and dynamic computer models

Computer models are widely used in scientific research to study and predict the behaviour of complex systems. The run times of computer-intensive simulators are often such that it is impractical to make the thousands of model runs that are conventionally required for sensitivity analysis, uncertainty analysis or calibration. In response to this problem, highly efficient techniques have recently been developed based on a statistical meta-model (the emulator) that is built to approximate the computer model. The approach, however, is less straightforward for dynamic simulators, designed to represent time-evolving systems. Generalisations of the established methodology to allow for dynamic emulation are here proposed and contrasted. Advantages and difficulties are discussed and illustrated with an application to the Sheffield Dynamic Global Vegetation Model, developed within the UK Centre for Terrestrial Carbon Dynamics.