Bayesian Updating of Parameters for a Sediment Entrainment Model via Markov Chain Monte Carlo
Publication: Journal of Hydraulic Engineering
Volume 135, Issue 1
Abstract
A Bayesian framework incorporating Markov chain Monte Carlo (MCMC) for updating the parameters of a sediment entrainment model is presented. Three subjects were pursued in this study. First, sensitivity analyses were performed via univariate MCMC. The results reveal that the posteriors resulting from two- and three-chain MCMC were not significantly different; two-chain MCMC converged faster than three chains. The proposal scale factor significantly affects the rate of convergence, but not the posteriors. The sampler outputs resulting from informed priors converged faster than those resulting from uninformed priors. The correlation coefficient of the Gram–Charlier (GC) probability density function (PDF) is a physical constraint imposed on MCMC in which a higher correlation would slow the rate of convergence. The results also indicate that the parameter uncertainty is reduced with increasing number of input data. Second, multivariate MCMC were carried out to simultaneously update the velocity coefficient and the statistical moments of the GC PDF. For fully rough flows, the distribution of was significantly modified via multivariate MCMC. However, for transitional regimes the posterior values of resulting from univariate and multivariate MCMC were not significantly different. For both rough and transitional regimes, the differences between the prior and posterior distributions of the statistical moments were limited. Third, the practical effect of updated parameters on the prediction of entrainment probabilities was demonstrated. With all the parameters updated, the sediment entrainment model was able to compute more accurately and realistically the entrainment probabilities. The present work offers an alternative approach to estimating the hydraulic parameters not easily observed.
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Acknowledgments
This study was supported in part by the National Science Council of TaiwanNSCT ROC. Comments from the editors and two anonymous reviewers helped to improve the clarity and completeness of this presentation.
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Published In
Journal of Hydraulic Engineering
Volume 135 • Issue 1 • January 2009
Pages: 22 - 37
Copyright
© 2009 ASCE.
History
Received: Mar 3, 2007
Accepted: Apr 15, 2008
Published online: Jan 1, 2009
Published in print: Jan 2009
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