Harnessing the Theoretical Foundations of the Exponential and Beta-Poisson Dose-Response Models to Quantify Parameter Uncertainty Using Markov Chain Monte Carlo

Risk Analysis ◽  
2013 ◽  
Vol 33 (9) ◽  
pp. 1677-1693 ◽  
Author(s):  
Philip J. Schmidt ◽  
Katarina D. M. Pintar ◽  
Aamir M. Fazil ◽  
Edward Topp
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Dose Response ◽  
Parameter Uncertainty ◽  
Response Models ◽  
Theoretical Foundations

Markov Chain Monte Carlo for Item Response Models

2017 ◽  
pp. 271-312
Author(s):  
Brian W. Junker ◽  
Richard J. Patz ◽  
Nathan M. VanHoudnos
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Item Response ◽  
Response Models ◽  
Item Response Models

Assessment of parameter uncertainty in hydrological model using a Markov-Chain-Monte-Carlo-based multilevel-factorial-analysis method

2016 ◽  
Vol 538 ◽  
pp. 471-486 ◽  
Author(s):  
Junlong Zhang ◽  
Yongping Li ◽  
Guohe Huang ◽  
Xi Chen ◽  
Anming Bao
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Uncertainty ◽  
Hydrological Model ◽  
Factorial Analysis ◽  
Analysis Method

Parallel Markov chain Monte Carlo for Bayesian dynamic item response models in educational testing

Stat ◽  
2017 ◽  
Vol 6 (1) ◽  
pp. 420-433 ◽  
Author(s):  
Zheng Wei ◽  
Xiaojing Wang ◽  
Erin Marie Conlon
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Item Response ◽  
Educational Testing ◽  
Response Models ◽  
Item Response Models

Improvement and comparison of likelihood functions for model calibration and parameter uncertainty analysis within a Markov chain Monte Carlo scheme

2014 ◽  
Vol 519 ◽  
pp. 2202-2214 ◽  
Author(s):  
Qin-Bo Cheng ◽  
Xi Chen ◽  
Chong-Yu Xu ◽  
Christian Reinhardt-Imjela ◽  
Achim Schulte
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Uncertainty Analysis ◽  
Parameter Uncertainty ◽  
Model Calibration ◽  
Likelihood Functions ◽  
Parameter Uncertainty Analysis

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.

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