Abstract
A Bayesian framework for model assessment, including an analysis of uncertainties due to small sample size, model inexactness and measurement error, was described in a paper by the first author in the previous IFIP Conference [1]. In this paper, we present computational methods for numerical evaluation of the statistical properties of the model parameters. These include efficient integration and simulation methods aimed at computing the marginal distributions and marginal and joint moments of the uncertain parameters. In the second part of the paper, the proposed methods are employed in evaluating several models recommended by the American Concrete Institute for design of concrete structures. To the authors’ knowledge, these applications are first attempts at rigorous evaluation of some widely used models in structural engineering.
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References
Der Kiureghian A. Bayesian analysis of model uncertainty in structural reliability. In Der Kiureghian A. and Thoft-Christensen P., editors, Reliability and Optimization of Structural Systems ‘80, Proceedings of the 3rd IFIP WG7.5 Conference, Berkeley, CA, pages 211–221, Berlin, Germany, 1990. Springer-Verlag.
Bard Y. Nonlinear Parameter Estimation. Academic Press, Orlando, Florida, 1974.
Box G.E.P. and Tiao G.C. Bayesian Inference in Statistical Analysis. Addison-Wesley, Reading, Massachusetts, USA, 1973.
Press S.J. Bayesian Statistics, Principles, Models, and Applications. John Wiley Sons, New York, 1989.
Naylor J.C. and Smith A.F.M. Applications of a method for the efficient computation of posterior distributions. Applied Statistics, 31 (3): 214–225, 1982.
Smith A.F.M., Skene A.M., Shaw J.E.II., and Naylor J.C. Progress with numerical and graphical methods for practical bayesian statistics. The Statistician, 36(): 75–82, 1987.
Engels II. Numerical Quadrature and Cubature. Academic Press, London, UK, 1980.
Rubinstein R.Y. Simulation and the Monte-Carlo method. John Wiley Sons, New York, USA, 1981.
Geweke J. Bayesian inference in econometric models using monte carlo integration. Econometrica, 57 (6): 1317–1339, 1989.
Van Dijck H.K., Kloek T., and Boender C.G. Posterior moments computed by mixed integration. Journal of Econometrics, 29(): 3–18, 1985.
Bjerager P. Probability integration by directional simulation. Journal of Engineering Mechanics, ASCE, 114 (8): 1285–1302, 1988.
Piessens R., de Doncker E., Überhuber C.W., and Kahaner D.K. Quadpack - a Subroutine Package for Automatic Integration. Springer-Verlag, Berlin, 1983.
Monteiro P.J.M., Moehle J.P., and Tang II.T. Aging effects on mechanical properties of power plant concretes. Technical report, Department of Civil Engineering, University of California at Berkeley, Berkeley, California, USA, 1990
Der Kiureghian A. Structural component reliability. Lecture notes for: Structural reliability - methods applications, Department of Civil Engineering, University of California at Berkeley, Berkeley, California, USA, 1989.
Ang A-S. and Tang W.H. Probability Concepts in Engineering Planning and Design. Volume I: Basic Principles. John Wiley Sons, New York, USA, 1975.
Der Kiureghian A. Measures of structural safety under imperfect states of knowledge. Journal of Structural Engineering, ASCE, 115 (5): 1119–1140, 1989.
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© 1992 International Federation for Information Processing, Geneva, Switzerland
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Geyskens, P., Der Kiureghian, A., Monteiro, P. (1992). Bayesian Model Assessment: Methods and Case Studies. In: Rackwitz, R., Thoft-Christensen, P. (eds) Reliability and Optimization of Structural Systems ’91. Lecture Notes in Engineering, vol 76. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84753-0_16
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DOI: https://doi.org/10.1007/978-3-642-84753-0_16
Publisher Name: Springer, Berlin, Heidelberg
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