Bayes Linear Emulation of Simulator Networks

Modern computational science allows complex scientific processes to be described by mathematical models implemented in computer codes, or simulators. When these simulators are computationally expensive, it is common to approximate them using statistical emulators constructed from computer experiments. Often, the overarching system of interest is best modelled via a chain, series or network of simulators, with inputs to some simulators arising as outputs from other simulators. Motivated by an epidemiological simulator chain to model the airborne dispersion of an infectious disease, we develop and assess novel methods for linking statistical emulators of the component simulators within a network. Our methods, Uncertain Input Sampling and Uncertain Input Bayes Linear Emulation, are developed within a Bayes linear framework and exploit the simpler structure that is typically observed for component simulators. They explicitly account for simulator input uncertainty induced by links in the network. 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 application. In all cases, significant gains were attained in terms of both predictive accuracy and computational expense.