Varying coefficient models and design choice for Bayes linear emulation of complex computer models with limited model evaluations

Computer models are widely used to help make decisions about real-world systems. As computer models of large and complex systems can have long run-times and high-dimensional input spaces it is often necessary to use emulation to assess uncertainties in computer model output. This paper presents methodology for emulation of complex computer models motivated by a real-world example in energy policy. The computer model studied is an economic model of investment inelectricity generation in Great Britain. The computer model was used to select parameters in a government policy designed to incentivise investment in renewable technologies to meet government targets. Limited computing time meant that few runs of the computer model were
available to fit an emulator. The statistical methodology developed was therefore focussed on accurately capturing the uncertainty in computer model output arising from the small number of available model runs. A varying coefficient emulator is proposed to model uncertainty in model output when extrapolating away from model runs. To maximise use of the small number of runs
available, this varying coefficient emulator is paired with a criterion-based procedure for design
selection.