Application of Markov Chain Monte Carlo Methodology to Reduction of Parameter Uncertainty in a Sediment Entrainment Model
Date Issued
2006
Date
2006
Author(s)
Chen, Chen-Chi
DOI
zh-TW
Abstract
This study investigates the application of Markov Chain Monte Carlo (MCMC) methodology to reduction of parameter uncertainty in a sediment entrainment model. Markov Chain Monte Carlo methodology is efficient for numerical Bayesian inference, particularly in high-dimension problems. In this work, a Bayesian framework of model parameters and outputs has been developed for updating model parameters by Markov Chain Monte Carlo methodology using the measured data. The results show that the parameter posterior distribution has a narrower range than the prior distribution, which means the parameter uncertainty is reduced. This study investigates the effect of different chain numbers and starting values on the convergence of MCMC. Little difference was observed between the results of two chains and three chains. This study also investigates the effect of different amount of data. Results show that the more data available, the more effective by the uncertainty is reduced. It is found that the posterior obtained by multiple-parameter updating is similar to those calculated by empirical formula and less prone to model inaccuracy than the posterior by single-parameter updating. To accelerate the computation speed, this study applies Monte Carlo integration to replace the traditional numerical adaptive quadrature. Results show that Monte Carlo integration effectively reduces computation time within the tolerance. As the sample number increases, the error decreases but the run time increases. This study uses the compromise programming to optimize the sample number.
Subjects
馬可夫鏈蒙地卡羅法
參數不確定性
數值貝氏推論
Markov Chain Monte Carlo
parameter uncertainty
numerical Bayesian inference
Type
thesis
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