A Semi-Automatic Method for History Matching using Sequential Monte Carlo

Abstract

The aim of the history matching method is to locate non-implausible regions of the parameter space of complex deterministic or stochastic models by matching model outputs with data. It does this via a series of waves where at each wave an emulator is fitted to a small number of training samples. An implausibility measure is defined which takes into account the closeness of simulated and observed outputs as well as emulator uncertainty. As the waves progress, the emulator becomes more accurate so that training samples are more concentrated on promising regions of the space and poorer parts of the space are rejected with more confidence. Whilst history matching has proved to be useful, existing implementations are not fully automated and some ad-hoc choices are made during the process, which involves user intervention and is time consuming. This occurs especially when the non-implausible region becomes small and it is difficult to sample this space uniformly to generate new training points. In this article we develop a sequential Monte Carlo (SMC) algorithm for implementation which is semi-automated. Our novel SMC approach reveals that the history matching method yields a non-implausible distribution that can be multi-modal, highly irregular and very difficult to sample uniformly. Our SMC approach offers a much more reliable sampling of the nonimplausible space, which requires additional computation compared to other approaches used in the literature.