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The inclusive and simplified forms of Bayesian interpolation for general and monotonic models using Gaussian and Generalized Beta distributions with application to Monte Carlo simulations

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  • Mohammadreza Rajabalinejad
  • Tew-Fik Mahdi

Abstract

A recently developed Bayesian interpolation method (BI) and its application to safety assessment of a flood defense structure are described in this paper. We use a one-dimensional Bayesian Monte Carlo method (BMC) that has been proposed in (Rajabalinejad 2009 ) to develop a weighted logical dependence between neighboring points. The concept of global uncertainty is adequately explained and different uncertainty association models (UAMs) are presented for linking the local and global uncertainty. Based on the global uncertainty, a simplified approach is introduced. By applying the global uncertainty, we apply the Guassian error estimation to general models and the Generalized Beta (GB) distribution to monotonic models. Our main objective in this research is to simplify the newly developed BMC method and demonstrate that it can dramatically improve the simulation efficiency by using prior information from outcomes of the preceding simulations. We provide theory and numerical algorithms for the BI method geared to multi-dimensional problems, integrate it with a probabilistic finite element model, and apply the coupled models to the reliability assessment of a flood defense for the 17th Street Flood Wall system in New Orleans. Copyright Springer Science+Business Media B.V. 2010

Suggested Citation

  • Mohammadreza Rajabalinejad & Tew-Fik Mahdi, 2010. "The inclusive and simplified forms of Bayesian interpolation for general and monotonic models using Gaussian and Generalized Beta distributions with application to Monte Carlo simulations," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 55(1), pages 29-49, October.
    • Handle: RePEc:spr:nathaz:v:55:y:2010:i:1:p:29-49
    DOI: 10.1007/s11069-010-9560-3
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    References listed on IDEAS

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    1. Rajabalinejad, M., 2010. "Bayesian Monte Carlo method," Reliability Engineering and System Safety, Elsevier, vol. 95(10), pages 1050-1060.
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    Cited by:

    1. Mohammadreza Rajabalinejad & Zeki Demirbilek & Tewfik Mahdi, 2010. "Determination of failure probabilities of flood defence systems with improved dynamic bounds method," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 55(1), pages 95-109, October.
    2. Mohammadreza Rajabalinejad & Tewfik Mahdi & Pieter Gelder, 2010. "Stochastic methods for safety assessment of the flood defense system in the Scheldt Estuary of the Netherlands," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 55(1), pages 123-144, October.

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