Optimization in the Space of Distribution Functions and Applications in the Bayes Analysis

  • Alexandr N. Golodnikov
  • Pavel S. Knopov
  • Panos M. Pardalos
  • Stanislav P. Uryasev
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 49)


This paper is stimulated by reliability estimation problems for safety systems of Nuclear Power Plants. A new approach for calculating robust Bayes estimators is considered. Upper and lower bounds for Bayes estimates, provided that a prior distribution satisfies available prior information, are constructed. The problems of calculating lower and upper bounds for Bayes estimates is reduced to optimization on a set of distributions satisfying available prior information. It was demonstrated that Bayes estimates of parameters are sensitive to the type of a prior distribution function. Analysis of the reliability data of a nuclear safety system was conducted using the developed methodology. The robust estimates were compared to Bayes estimates traditionally used in nuclear industry.


Prior Distribution Beta Estimate Binomial Sampling Robust Bayesian Analysis Reliability Parameter Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Alexandr N. Golodnikov
    • 1
  • Pavel S. Knopov
    • 1
  • Panos M. Pardalos
    • 2
  • Stanislav P. Uryasev
    • 3
  1. 1.V. M. Glushkov Institute of CyberneticsKievUkraine
  2. 2.Center for Applied Optimization and ISE DepartmentUniversity of FloridaGainesvilleUSA
  3. 3.ISE DepartmentUniversity of FloridaGainesvilleUSA

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