Postaudit evaluation of conceptual model uncertainty for a glacial aquifer groundwater flow and contaminant transport model

Lemke, Lawrence D.; Cypher, Joseph A.

doi:10.1007/s10040-009-0554-8

Cited by 7 publications

(1 citation statement)

References 13 publications

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“…The thermodynamic integration method is also applied to a synthetic case of groundwater modeling. The synthetic case considers four alternative models postulated for different conceptualizations of a confining layer, a commonly encountered conceptual model uncertainty in groundwater modeling [ Lemke and Cypher , ]. The four models have a relatively large number of parameters, ranging from 12 to 21, which is common in groundwater modeling.…”

Section: Introductionmentioning

confidence: 99%

Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods

Liu

Elshall

et al. 2016

Water Resources Research

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Evaluating marginal likelihood is the most critical and computationally expensive task, when conducting Bayesian model averaging to quantify parametric and model uncertainties. The evaluation is commonly done by using Laplace approximations to evaluate semianalytical expressions of the marginal likelihood or by using Monte Carlo (MC) methods to evaluate arithmetic or harmonic mean of a joint likelihood function. This study introduces a new MC method, i.e., thermodynamic integration, which has not been attempted in environmental modeling. Instead of using samples only from prior parameter space (as in arithmetic mean evaluation) or posterior parameter space (as in harmonic mean evaluation), the thermodynamic integration method uses samples generated gradually from the prior to posterior parameter space. This is done through a path sampling that conducts Markov chain Monte Carlo simulation with different power coefficient values applied to the joint likelihood function. The thermodynamic integration method is evaluated using three analytical functions by comparing the method with two variants of the Laplace approximation method and three MC methods, including the nested sampling method that is recently introduced into environmental modeling. The thermodynamic integration method outperforms the other methods in terms of their accuracy, convergence, and consistency. The thermodynamic integration method is also applied to a synthetic case of groundwater modeling with four alternative models. The application shows that model probabilities obtained using the thermodynamic integration method improves predictive performance of Bayesian model averaging. The thermodynamic integration method is mathematically rigorous, and its MC implementation is computationally general for a wide range of environmental problems.

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Section: Introductionmentioning

confidence: 99%

Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods

Liu

Elshall

et al. 2016

Water Resources Research

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Vertical hydraulic conductivity and layered heterogeneity: from measurements to models

Shepley

2024

Hydrogeol J

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Studies on effects of traffic tunnels on the migration of the contaminants under landfill sites

Yang

Jin

2019

Environ Sci Pollut Res

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Postaudit evaluation of conceptual model uncertainty for a glacial aquifer groundwater flow and contaminant transport model

Cited by 7 publications

References 13 publications

Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods

Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods

Vertical hydraulic conductivity and layered heterogeneity: from measurements to models

Studies on effects of traffic tunnels on the migration of the contaminants under landfill sites

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