Estimation of spatial covariance structures by adjoint state maximum likelihood cross validation: 2. Synthetic experiments

Samper, F. Javier; Neuman, S. P.

doi:10.1029/wr025i003p00363

Cited by 26 publications

(15 citation statements)

References 9 publications

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“…Whereas is obtained through expansion of p ( D ∣ k , M k ) and p ( θ k ∣ M k ) in Taylor series about k , the Laplace approximation follows from an asymptotic expansion of the integral . As mentioned in the Introduction, we prefer because it conforms more directly to ML‐based hydrologic model discrimination and parameter estimation frameworks proposed for deterministic models by Carrera and Neuman [1986a, 1986b], for geostatistical models by Samper and Neuman [1989a, 1989b], and for stochastic moment models by Hernandez et al [2002, 2003].…”

Section: Maximum Likelihood Bayesian Model Averaging (Mlbma)mentioning

confidence: 99%

“…Previously, KIC k has been used [e.g., Carrera and Neuman , 1986a, 1998b; Samper and Neuman , 1989a, 1989b] as an optimum decision rule for the ranking of competing models. The highest‐ranking model is that corresponding to KIC min .…”

Section: Maximum Likelihood Bayesian Model Averaging (Mlbma)mentioning

confidence: 99%

“…Analyses of model uncertainty based on a single hydrologic concept are prone to statistical bias (by committing a type II error through reliance on an invalid model) and underestimation of uncertainty (by committing a type I error through under sampling of the relevant model space). Carrera and Neuman [1986a, 1986b] and Samper and Neuman [1989a, 1989b] have noted that bias and uncertainty resulting from an inadequate model structure (conceptualization) are far more detrimental to the model's predictive ability than is a suboptimal set of model parameters. Yet most hydrologic analyses ignore structural uncertainty and focus exclusively on the optimization of model parameters.…”

Section: Introductionmentioning

confidence: 99%

“… Kashyap 's [1982] expression is closely related to an ML version of the Laplace approximation [e.g., Draper , 1995; Kass and Raftery , 1995] used successfully in the BMA context by statisticians [ Hoeting et al , 1999]. We prefer the former because it conforms more directly to ML‐based hydrologic model discrimination and parameter estimation frameworks proposed for deterministic models by Carrera and Neuman [1986a, 1986b], for geostatistical models by Samper and Neuman [1989a, 1989b], and for stochastic moment models by Hernandez et al [2002, 2003].…”

Section: Introductionmentioning

confidence: 99%

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Maximum likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff

Neuman

Meyer

2004

Water Resources Research

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[1] Hydrologic analyses typically rely on a single conceptual-mathematical model. Yet hydrologic environments are open and complex, rendering them prone to multiple interpretations and mathematical descriptions. Adopting only one of these may lead to statistical bias and underestimation of uncertainty. Bayesian model averaging (BMA) [Hoeting et al., 1999] provides an optimal way to combine the predictions of several competing models and to assess their joint predictive uncertainty. However, it tends to be computationally demanding and relies heavily on prior information about model parameters. Neuman [2002, 2003] proposed a maximum likelihood version (MLBMA) of BMA to render it computationally feasible and to allow dealing with cases where reliable prior information is lacking. We apply MLBMA to seven alternative variogram models of log air permeability data from single-hole pneumatic injection tests in six boreholes at the Apache Leap Research Site (ALRS) in central Arizona. Unbiased ML estimates of variogram and drift parameters are obtained using adjoint state maximum likelihood cross validation [Samper and Neuman, 1989a] in conjunction with universal kriging and generalized least squares. Standard information criteria provide an ambiguous ranking of the models, which does not justify selecting one of them and discarding all others as is commonly done in practice. Instead, we eliminate some of the models based on their negligibly small posterior probabilities and use the rest to project the measured log permeabilities by kriging onto a rock volume containing the six boreholes. We then average these four projections and associated kriging variances, using the posterior probability of each model as weight. Finally, we cross validate the results by eliminating from consideration all data from one borehole at a time, repeating the above process and comparing the predictive capability of MLBMA with that of each individual model. We find that MLBMA is superior to any individual geostatistical model of log permeability among those we consider at the ALRS.

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Section: Maximum Likelihood Bayesian Model Averaging (Mlbma)mentioning

confidence: 99%

Section: Maximum Likelihood Bayesian Model Averaging (Mlbma)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Maximum likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff

Neuman

Meyer

2004

Water Resources Research

Self Cite

190

240

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“…The need to move away from one 'optimal' model (or parameter set) to a set of multiple models for predictions was identified early on by Delhomme (1979), Neuman (1982, Hoeksema and Kitanidis (1989), Wagner and Gorelick (1989), Beven (1993), and Neuman and Wierenga (2003) among others. It has been shown that considering a single conceptual model for a site can lead to biased and erroneous results that handicap environmental and economic decision making (National Research Council 2001;Neuman and Wierenga 2003;Carrera and Neuman 1986;Samper and Neuman 1989). Instead, it is recommended that a set of acceptable and realistic model representations that are consistent with the data are used for predictive analysis.…”

Section: Background On Uncertainty Analysismentioning

confidence: 96%

Incorporating subjective and stochastic uncertainty in an interactive multi-objective groundwater calibration framework

Singh¹,

Walker

Minsker

et al. 2010

Stoch Environ Res Risk Assess

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The interactive multi-objective genetic algorithm (IMOGA) combines traditional optimization with an interactive framework that considers the subjective knowledge of hydro-geological experts in addition to quantitative calibration measures such as calibration errors and regularization to solve the groundwater inverse problem. The IM-OGA is inherently a deterministic framework and identifies multiple large-scale parameter fields (typically head and transmissivity data are used to identify transmissivity fields). These large-scale parameter fields represent the optimal trade-offs between the different criteria (quantitative and qualitative) used in the IMOGA. This paper further extends the IMOGA to incorporate uncertainty both in the large-scale trends as well as the small-scale variability (which can not be resolved using the field data) in the parameter fields. The different parameter fields identified by the IMOGA represent the uncertainty in large-scale trends, and this uncertainty is modeled using a Bayesian approach where calibration error, regularization, and the expert's subjective preference are combined to compute a likelihood metric for each parameter field. Small-scale (stochastic) variability is modeled using a geostatistical approach and added onto the large-scale trends identified by the IMOGA. This approach is applied to the Waste Isolation Pilot Plant (WIPP) case-study. Results, with and without expert interaction, are analyzed and the impact that expert judgment has on predictive uncertainty at the WIPP site is discussed. It is shown that for this case, expert interaction leads to more conservative solutions as the expert compensates for some of the lack of data and modeling approximations introduced in the formulation of the problem.

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Multimodel framework for characterization of transport in porous media

Ciriello

Edery

Guadagnini

et al. 2015

Water Resources Research

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We consider modeling approaches to characterize solute transport in porous media, integrating them into a unique theoretical and experimental framework for model evaluation and data interpretation. To date, development of (conservative and reactive chemical) transport models and formulation of model calibration methods grounded on sensitivity-based collection of measurements have been pursued in parallel. Key questions that remain include: For a given set of measurements, which conceptual picture of the transport processes, as embodied in a mathematical model or models, is most appropriate? What are the most valuable space-time locations for solute concentration measurements, depending on the model selected? How is model parameter uncertainty propagated to model output, and how does this propagation affect model calibration? We address these questions by merging parallel streams of research-model formulation, reduction, calibration, sensitivity analysis, and discrimination-offering our view on an emerging framework that guides (i) selection of an appropriate number and location of time-dependent concentration measurements given a transport model and (ii) assessment (through discrimination criteria) of the relative benefit of applying any particular model from a set of several models. Our strategy is to employ metrics to quantify the relative contribution of each uncertain model parameter to the variability of the model output. We evaluate these metrics through construction of a surrogate (or ''meta'') transport model that has the additional benefit of enabling sensitivity analysis and model calibration at a highly reduced computational cost. We demonstrate the applicability of this framework, focusing on transport of reactive chemicals in laboratory-scale porous media.

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Estimation of spatial covariance structures by adjoint state maximum likelihood cross validation: 2. Synthetic experiments

Cited by 26 publications

References 9 publications

Maximum likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff

Maximum likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff

Incorporating subjective and stochastic uncertainty in an interactive multi-objective groundwater calibration framework

Multimodel framework for characterization of transport in porous media

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