Computer model evaluation studies aim to 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.

Software and complete information needed to recapitulate the analyses reported are available to interested readers. This archive contains the data and the Matlab code to conduct the analysis, together with a readme note on use of the code.

This research was supported in part by the Statistical and Applied Mathematical Sciences Institute (SAMSI) 2006-7 research program on Development, Assessment and Utilization of Complex Computer Models and by the University of Missouri-Columbia summer research fellowship. The computer model data used in this paper was kindly provided by Peter Reichert. The first author would like to thank Dr. James Berger for his advisory during her Ph.D. study at Duke University. We also thank the editor and reviewers for comments on the original version of the paper. Research of Mike West was partially supported by National Science Foundation (DMS-0342172). Further, the final versions of this research were partly supported during the Sequential Monte Carlo program at SAMSI under the National Science Foundation Grant DMS-0635449. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Any opinions, findings and conclusions or recommendations expressed in this work are those of the authors and do not necessarily reflect the views of the NSF.