Generalising history matching for enhanced calibration of computer models

Abstract

History matching using Gaussian process emulators is a well-known methodology for the calibration of computer models. It attempts to identify the parts of input parameter space that are likely to result in mismatches between simulator outputs and physical observations by using emulators. These parts are then ruled out. The remaining “Not Ruled Out Yet (NROY)” input space is then searched for good matches by repeating the history matching process. The first section of this thesis illustrates an easily neglected limitation of standard history matching: the emulator must simulate the target NROY space well, else good parameter choices can be ruled out. We show that even when an emulator passes standard diagnostic checks on the whole parameter space, good parameter choices can easily be ruled out. We present novel methods for detecting these cases and a Local Voronoi Tessellation method for a robust approach to calibration that ensures that the true NROY space is retained and parameter inference is not biased. The remainder of this thesis looks into developing a generalised history matching for calibrating computer models with high-dimensional output. We address another limitation of the standard (PCA-based) history matching, which only works well when the parameters are responsible for the strength of various patterns. We show that when the parameters control the position of patterns, e.g. shifting currents, current approaches will not generally be able to calibrate these models. To overcome this, we extend history matching to kernel feature space, where output space for moving patterns can be compared with the observations. We develop kernel-based history matching as a generalisation to history matching and examine the multiple possible interpretations of the usual implausibility measure and threshold for defining NROY. Automatic kernel selection based on expert modeller judgement is introduced to enable the experts to define important features that the model should be able to reproduce.