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Mechanism-based emulation of dynamic simulation models: Concept and application in hydrology

Author

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  • Reichert, P.
  • White, G.
  • Bayarri, M.J.
  • Pitman, E.B.

Abstract

Many model-based investigation techniques, such as sensitivity analysis, optimization, and statistical inference, require a large number of model evaluations to be performed at different input and/or parameter values. This limits the application of these techniques to models that can be implemented in computationally efficient computer codes. Emulators, by providing efficient interpolation between outputs of deterministic simulation models, can considerably extend the field of applicability of such computationally demanding techniques. So far, the dominant techniques for developing emulators have been priors in the form of Gaussian stochastic processes (GASP) that were conditioned with a design data set of inputs and corresponding model outputs. In the context of dynamic models, this approach has two essential disadvantages: (i) these emulators do not consider our knowledge of the structure of the model, and (ii) they run into numerical difficulties if there are a large number of closely spaced input points as is often the case in the time dimension of dynamic models. To address both of these problems, a new concept of developing emulators for dynamic models is proposed. This concept is based on a prior that combines a simplified linear state space model of the temporal evolution of the dynamic model with Gaussian stochastic processes for the innovation terms as functions of model parameters and/or inputs. These innovation terms are intended to correct the error of the linear model at each output step. Conditioning this prior to the design data set is done by Kalman smoothing. This leads to an efficient emulator that, due to the consideration of our knowledge about dominant mechanisms built into the simulation model, can be expected to outperform purely statistical emulators at least in cases in which the design data set is small. The feasibility and potential difficulties of the proposed approach are demonstrated by the application to a simple hydrological model.

Suggested Citation

  • Reichert, P. & White, G. & Bayarri, M.J. & Pitman, E.B., 2011. "Mechanism-based emulation of dynamic simulation models: Concept and application in hydrology," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1638-1655, April.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1638-1655
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    References listed on IDEAS

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    1. S. Conti & J. P. Gosling & J. E. Oakley & A. O'Hagan, 2009. "Gaussian process emulation of dynamic computer codes," Biometrika, Biometrika Trust, vol. 96(3), pages 663-676.
    2. Jeremy Oakley, 2002. "Bayesian inference for the uncertainty distribution of computer model outputs," Biometrika, Biometrika Trust, vol. 89(4), pages 769-784, December.
    3. Marc C. Kennedy & Anthony O'Hagan, 2001. "Bayesian calibration of computer models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 425-464.
    4. Craig P. S & Goldstein M. & Rougier J. C & Seheult A. H, 2001. "Bayesian Forecasting for Complex Systems Using Computer Simulators," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 717-729, June.
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    1. repec:eee:csdana:v:56:y:2012:i:12:p:3959-3974 is not listed on IDEAS
    2. Nott, David J. & Marshall, Lucy & Fielding, Mark & Liong, Shie-Yui, 2014. "Mixtures of experts for understanding model discrepancy in dynamic computer models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 491-505.
    3. Auffray, Yves & Barbillon, Pierre & Marin, Jean-Michel, 2014. "Bounding rare event probabilities in computer experiments," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 153-166.

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