  Computationally expensive simulators, implementing mathematical models in
computer codes, are commonly approximated using statistical emulators. We
develop and assess novel emulation methods for systems best modelled via a
chain, series or network of simulators. Using a Bayes linear framework, we link
statistical emulators of the component simulators to explicitly account for the
simulator input uncertainty induced by links between models in arbitrarily
large networks. We demonstrate the advantages of these methods compared to use
of a single emulator of the composite simulator network for a variety of
examples, including the motivating epidemiological simulator chain to model the
impact of an airborne infectious disease.
