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Summary  We present a common framework for Bayesian emulation methodologies for multivariate output simulators, or computer models, that employ either parametric linear models or non‐parametric Gaussian processes. Novel diagnostics suitable for multivariate covariance separable emulators are developed and techniques to improve the adequacy of an emulator are discussed and implemented. A variety of emulators are compared for a humanitarian relief simulator, modelling aid missions to Sicily after a volcanic eruption and earthquake, and a sensitivity analysis is conducted to determine the sensitivity of the simulator output to changes in the input variables. The results from parametric and non‐parametric emulators are compared in terms of prediction accuracy, uncertainty quantification and scientific interpretability.

Multivariate emulation of computer simulators: model selection and diagnostics with application to a humanitarian relief model