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Excursions in the Bayesian treatment of model error

Author

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  • L Mark Berliner
  • Radu Herbei
  • Christopher K Wikle
  • Ralph F Milliff

Abstract

Advances in observational and computational assets have led to revolutions in the range and quality of results in many science and engineering settings. However, those advances have led to needs for new research in treating model errors and assessing their impacts. We consider two settings. The first involves physically-based statistical models that are sufficiently manageable to allow incorporation of a stochastic “model error process”. In the second case we consider large-scale models in which incorporation of a model error process and updating its distribution is impractical. Our suggestion is to treat dimension-reduced model output as if it is observational data, with a data model that incorporates a bias component to represent the impacts of model error. We believe that our suggestions are valuable quantitative, yet relatively simple, ways to extract useful information from models while including adjustment for model error. These ideas are illustrated and assessed using an application inspired by a classical oceanographic problem.

Suggested Citation

  • L Mark Berliner & Radu Herbei & Christopher K Wikle & Ralph F Milliff, 2023. "Excursions in the Bayesian treatment of model error," PLOS ONE, Public Library of Science, vol. 18(6), pages 1-22, June.
    • Handle: RePEc:plo:pone00:0286624
    DOI: 10.1371/journal.pone.0286624
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    References listed on IDEAS

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    1. James Berger & Elías Moreno & Luis Pericchi & M. Bayarri & José Bernardo & Juan Cano & Julián Horra & Jacinto Martín & David Ríos-Insúa & Bruno Betrò & A. Dasgupta & Paul Gustafson & Larry Wasserman &, 1994. "An overview of robust Bayesian analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(1), pages 5-124, June.
    2. David T. Frazier & Christian P. Robert & Judith Rousseau, 2020. "Model misspecification in approximate Bayesian computation: consequences and diagnostics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(2), pages 421-444, April.
    3. 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.
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