Comparing multiple simulators using Bayesian emulators

Abstract

Bayesian emulation has proved to be a useful tool for working with complicated, high dimensional simulators, approximating the simulator's behaviour in a probabilistic way, enabling operations such as prediction or calibration, and therefore providing an ecient approximation to the simulator's representation of the system.
Complex systems, however, are often modelled by several different simulators, each with dierent strengths and weaknesses. Combining them to better understand the system, or comparing their behaviour as functions, is very dicult. This is largely because their input spaces cannot be directly linked.
In this thesis, we present two methods for using emulation to jointly model two simulators, allowing them to be compared. We also introduce two simulators of the ocean carbon cycle, OG99NPZD and HadOCC. The ocean carbon cycle is of interest largely because it concerns the biological processes by which some carbon is stored in the deep ocean. These simulators have dierent input spaces and model the system dierently, and standard emulation proves to be unable to compare them.
The first method for two simulators, hierarchical emulation, works with pairs of simulators for which one is an extension of the other, and therefore whose input spaces are mostly similar. This uses the relationship between the simulators to emulate the more complex as a sum of the simpler simulator and some newly created functions. Validation studies using hierarchical emulators to model two versions of HadOCC show that the hierarchical emulator outperforms the standard methods in modelling both the extended simulator and the dierence between the two.
The second, intermediate variable emulation, makes no constraint on the relationship between the simulators, instead making connections using sub-processes represented in both. This allows the representations of a system by two simulators to be directly compared; the contributions of the dierent sub-processes can be contrasted, and the sub-processes themselves can be used to gain better understanding of the relationship between the two input spaces. Intermediate variable emulators are used to compare OG99NPZD and HadOCC.
Finally, to enable an ecient and robust implementation of these methods, as well as of the standard emulation method, an object-oriented framework for emulation is presented.