Bayesian Updating of Parameters for a Sediment Entrainment Model via Markov Chain Monte Carlo

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