Using Bayes Linear Emulators to Analyse Networks of Simulators
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The key dynamics of processes within physical systems are often represented in the form of computer models, or simulators. Often, the overarching system of interest, comprising of multiple processes, may be represented as a network of simulators, with some of the inputs to some simulators arising from the outputs to other simulators. Much of the computational statistics literature focusses on approximating computationally intensive simulators using statistical emulators. An important, yet underexplored question in this literature is: can emulating the individual simulators within a network be more powerful than emulating the composite simulator network as a single simulator? In this article we present two novel approaches for linking Bayes linear emulators of several component simulators together to obtain an approximation for the composite simulator, comparing these ideas to approximating the composite simulator using a single emulator. These techniques, termed the Bayes linear sampling approach and Uncertain Input Bayes linear emulator, will be demonstrated on a couple of illustrative simulated examples, as well as being applied to an important dispersion dose-response chain of simulators used for disease modelling.
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