Using Markov Chain Monte Carlo to quantify parameter uncertainty and its effect on predictions of a groundwater flow model

2009 ◽  
Vol 24 (6) ◽  
pp. 749-763 ◽  
Author(s):  
Ahmed E. Hassan ◽  
Hesham M. Bekhit ◽  
Jenny B. Chapman
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Groundwater Flow ◽  
Parameter Uncertainty ◽  
Flow Model ◽  
Groundwater Flow Model

scholarly journals Nonlinear Parameter Estimation: Comparison of an Ensemble Kalman Smoother with a Markov Chain Monte Carlo Algorithm

2012 ◽  
Vol 140 (6) ◽  
pp. 1957-1974 ◽  
Author(s):  
Derek J. Posselt ◽  
Craig H. Bishop
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Uncertainty ◽  
Posterior Probability ◽  
Monte Carlo Algorithm ◽  
Parameter Estimates ◽  
Posterior Probability Distribution ◽  
Kalman Smoother ◽  
Non Gaussian

Abstract This paper explores the temporal evolution of cloud microphysical parameter uncertainty using an idealized 1D model of deep convection. Model parameter uncertainty is quantified using a Markov chain Monte Carlo (MCMC) algorithm. A new form of the ensemble transform Kalman smoother (ETKS) appropriate for the case where the number of ensemble members exceeds the number of observations is then used to obtain estimates of model uncertainty associated with variability in model physics parameters. Robustness of the parameter estimates and ensemble parameter distributions derived from ETKS is assessed via comparison with MCMC. Nonlinearity in the relationship between parameters and model output gives rise to a non-Gaussian posterior probability distribution for the parameters that exhibits skewness early and multimodality late in the simulation. The transition from unimodal to multimodal posterior probability density function (PDF) reflects the transition from convective to stratiform rainfall. ETKS-based estimates of the posterior mean are shown to be robust, as long as the posterior PDF has a single mode. Once multimodality manifests in the solution, the MCMC posterior parameter means and variances differ markedly from those from the ETKS. However, it is also shown that if the ETKS is given a multimode prior ensemble, multimodality is preserved in the ETKS posterior analysis. These results suggest that the primary limitation of the ETKS is not the inability to deal with multimodal, non-Gaussian priors. Rather it is the inability of the ETKS to represent posterior perturbations as nonlinear functions of prior perturbations that causes the most profound difference between MCMC posterior PDFs and ETKS posterior PDFs.

Quantifying parameter uncertainty in a coral reef model using Metropolis-Coupled Markov Chain Monte Carlo

2010 ◽  
Vol 221 (10) ◽  
pp. 1337-1347 ◽  
Author(s):  
Damian Clancy ◽  
Jason E. Tanner ◽  
Stephen McWilliam ◽  
Matthew Spencer
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Coral Reef ◽  
Markov Chain Monte Carlo ◽  
Parameter Uncertainty
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