A Dynamic Modelling Strategy for Bayesian Computer Model Emulation

Computer model evaluation studies build statistical models of deterministic simulation-based predictions of field data to then assess and criticize the computer model and suggest refinements. Computer models are often expensive computationally: statistical models that adequately emulate their key features can be very much more efficient. Gaussian process models are often used as emulators, but the resulting computations lack the ability to scale to higher-dimensional, time-dependent or functional outputs. For some such problems, especially for contexts of time series outputs, building emulators using dynamic linear models provides a computationally attractive alternative as well as a flexible modelling approach capable of emulating a broad range of stochastic structures underlying the input-output simulations. We describe this here, combining Bayesian multivariate dynamic linear models with Gaussian process modelling in an effective manner, and illustrate the approach with data from a hydrological simulation model. The general strategy will be useful for other computer model evaluation studies with time series or functional outputs.