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
non-implausible space, which requires additional computation compared to other
approaches used in the literature
