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Structural Engineering and Mechanics
  Volume 25, Number 3, February20 2007 , pages 331-345

Probabilistic assessment on the basis of interval data
Ben H. Thacker and Luc J. Huyse

    Uncertainties enter a complex analysis from a variety of sources: variability, lack of data, human errors, model simplification and lack of understanding of the underlying physics. However, for many important engineering applications insufficient data are available to justify the choice of a particular probability density function (PDF). Sometimes the only data available are in the form of interval estimates which represent, often conflicting, expert opinion. In this paper we demonstrate that Bayesian estimation techniques can successfully be used in applications where only vague interval measurements are available. The proposed approach is intended to fit within a probabilistic framework, which is established and widely accepted. To circumvent the problem of selecting a specific PDF when only little or vague data are available, a hierarchical model of a continuous family of PDF?s is used. The classical Bayesian estimation methods are expanded to make use of imprecise interval data. Each of the expert opinions (interval data) are interpreted as random interval samples of a parent PDF. Consequently, a partial conflict between experts is automatically accounted for through the likelihood function.
Key Words
    modal uncertainty; interval data; Beyesian analysis; expert knowledge; conflicting data
Ben H. Thacker and Luc J. Huyse; Materials Engineering Department, Southwest Research Institute,
6220 Culebra Road, San Antonio, Texas, USA

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