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Validation of imprecise probability models

Author

Listed:
  • Scott Ferson
  • William L. Oberkampf

Abstract

Validation is the assessment of the match between a model's predictions and empirical observations. It can be complex when either data or the prediction is characterised as an uncertain number (i.e. interval, probability distribution, p-box, or more general structure). Validation could measure the discrepancy between the shapes of the two uncertain numbers representing prediction and data, or it could characterise the differences between realisations drawn from the respective uncertain numbers. The unification between these two concepts relies on defining the validation measure between prediction and data as the shortest possible distance given the imprecision about the distributions and their dependencies.

Suggested Citation

  • Scott Ferson & William L. Oberkampf, 2009. "Validation of imprecise probability models," International Journal of Reliability and Safety, Inderscience Enterprises Ltd, vol. 3(1/2/3), pages 3-22.
    • Handle: RePEc:ids:ijrsaf:v:3:y:2009:i:1/2/3:p:3-22
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    Citations

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    Cited by:

    1. Bin Suo & Yang Qi & Kai Sun & Jingyuan Xu, 2023. "A Novel Model Validation Method Based on Area Metric Disagreement between Accelerated Storage Distributions and Natural Storage Data," Mathematics, MDPI, vol. 11(11), pages 1-18, May.
    2. Ling, You & Mahadevan, Sankaran, 2013. "Quantitative model validation techniques: New insights," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 217-231.
    3. Ao, Dan & Hu, Zhen & Mahadevan, Sankaran, 2017. "Design of validation experiments for life prediction models," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 22-33.
    4. Zhao, Lufeng & Lu, Zhenzhou & Yun, Wanying & Wang, Wenjin, 2017. "Validation metric based on Mahalanobis distance for models with multiple correlated responses," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 80-89.
    5. Li, Wei & Chen, Wei & Jiang, Zhen & Lu, Zhenzhou & Liu, Yu, 2014. "New validation metrics for models with multiple correlated responses," Reliability Engineering and System Safety, Elsevier, vol. 127(C), pages 1-11.
    6. Mullins, Joshua & Ling, You & Mahadevan, Sankaran & Sun, Lin & Strachan, Alejandro, 2016. "Separation of aleatory and epistemic uncertainty in probabilistic model validation," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 49-59.
    7. Wu, Danqing & Lu, Zhenzhou & Wang, Yanping & Cheng, Lei, 2015. "Model validation and calibration based on component functions of model output," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 59-70.
    8. Liu, Yang & Wang, Dewei & Sun, Xiaodong & Liu, Yang & Dinh, Nam & Hu, Rui, 2021. "Uncertainty quantification for Multiphase-CFD simulations of bubbly flows: a machine learning-based Bayesian approach supported by high-resolution experiments," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    9. Wang, Chong & Matthies, Hermann G., 2019. "Novel model calibration method via non-probabilistic interval characterization and Bayesian theory," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 84-92.
    10. McKeand, Austin M. & Gorguluarslan, Recep M. & Choi, Seung-Kyum, 2021. "Stochastic analysis and validation under aleatory and epistemic uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    11. Li, Chenzhao & Mahadevan, Sankaran, 2016. "Role of calibration, validation, and relevance in multi-level uncertainty integration," Reliability Engineering and System Safety, Elsevier, vol. 148(C), pages 32-43.
    12. Mathieu Balesdent & Jérôme Morio & Loïc Brevault, 2016. "Rare Event Probability Estimation in the Presence of Epistemic Uncertainty on Input Probability Distribution Parameters," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 197-216, March.
    13. Kwag, Shinyoung & Gupta, Abhinav & Dinh, Nam, 2018. "Probabilistic risk assessment based model validation method using Bayesian network," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 380-393.

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