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Mixtures of experts for understanding model discrepancy in dynamic computer models

Author

Listed:
  • Nott, David J.
  • Marshall, Lucy
  • Fielding, Mark
  • Liong, Shie-Yui

Abstract

There are many areas of science and engineering where research and decision making are performed using computer models. These computer models are usually deterministic and may take minutes, hours or days to produce an output for a single value of the model inputs. Fitting mixtures of experts of computer models where the expert components use different values of the computer model parameters is considered. The efficient calibration of such models using emulators, which are fast statistical surrogates for the computer model, is discussed. It is argued that mixtures of experts are often insightful for describing model discrepancy and ways in which the computer model can be improved. This is not a strength of standard approaches to the statistical analysis of computer models where a certain “best input” assumption is usually made and model discrepancy is often described through a stationary Gaussian process prior on the discrepancy function. Application of the framework is presented for a dynamic hydrological rainfall–runoff model in which the mixture approach is helpful for highlighting model deficiencies.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:491-505
    DOI: 10.1016/j.csda.2013.04.020
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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. Higdon, Dave & Gattiker, James & Williams, Brian & Rightley, Maria, 2008. "Computer Model Calibration Using High-Dimensional Output," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 570-583, June.
    3. 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.
    4. 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.
    5. 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.
    6. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
    7. Alexandre X. Carvalho & Martin A. Tanner, 2006. "Modeling nonlinearities with mixtures-of-experts of time series models," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-22, August.
    8. Goldstein, Michael & Rougier, Jonathan, 2006. "Bayes Linear Calibrated Prediction for Complex Systems," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1132-1143, September.
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