Bayesian assessment of the expected data impact on prediction confidence in optimal sampling design

Leube, P.; Geiges, A.; Nowak, Wolfgang

doi:10.1029/2010wr010137

Cited by 69 publications

(92 citation statements)

References 71 publications

(98 reference statements)

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“…We obtain the prior arrival time probability distribution pðÞ via Monte Carlo simulation with n r ¼ 40;000 realizations, based on the parameter values listed in Table 3. To evaluate all the possible conditional distributions of travel time pðjyÞ for any possible data set y, the required test statistics and the objective function (equation (10)) according to the scheme outlined in sections A2 and A1, we use the PreDIA framework by Leube et al [2012].…”

Section: Methodsmentioning

confidence: 99%

“…These actual information needs would be represented only inaccurately by surrogate criteria such as the variance of . for example, Leube et al [2012] demonstrate in a synthetic case study that optimal designs are significantly different when optimized to minimize the prediction variance of contaminant concentrations or to minimize the prediction variance of a corresponding indicator variable I : c ! c 0 .…”

Section: Preposterior Stage and Reliability Of A Designmentioning

confidence: 99%

“…In some situations, analytical solutions and linearized approaches are inappropriate. For such reasons we recommend fully nonlinear and fully Bayesian evaluation schemes based on well-designed Monte Carlo analysis, such as the PreDIA framework [e.g., Leube et al, 2012] based on bootstrap or particle filtering [e.g., Efron, 1982;Gordon et al, 1993] or the method of anchored distributions [e.g., Rubin et al, 2010].…”

Section: A1 Conditional Simulation and Bayesian Inferencementioning

confidence: 99%

“…It can be used to optimize (1) what types of data (e.g., material parameters, state variables) to collect, (2) where to sample (e.g., the spatial layout and time schedule of observation networks), and (3) how to best excite the system to observe an informative response (e.g., designing tracer injections or hydraulic tests). Many applications in groundwater hydrology can be found in the literature [e.g., James and Gorelick, 1994;Reed et al, 2000a;Herrera and Pinder, 2005;Nowak et al, 2010;Leube et al, 2012].…”

Section: Introductionmentioning

confidence: 99%

“…This task calls for nonlinear Bayesian inference schemes such as PreDIA [Leube et al, 2012] (see also sections 4.3 and Ax).…”

Section: Hypothesis-driven Optimal Designmentioning

confidence: 99%

See 4 more Smart Citations

A hypothesis‐driven approach to optimize field campaigns

Nowak¹,

Rubin²,

Barros³

2012

Water Resources Research

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[1] Most field campaigns aim at helping in specified scientific or practical tasks, such as modeling, prediction, optimization, or management. Often these tasks involve binary decisions or seek answers to yes/no questions under uncertainty, e.g., Is a model adequate? Will contamination exceed a critical level? In this context, the information needs of hydro(geo)logical modeling should be satisfied with efficient and rational field campaigns, e.g., because budgets are limited. We propose a new framework to optimize field campaigns that defines the quest for defensible decisions as the ultimate goal. The key steps are to formulate yes/no questions under uncertainty as Bayesian hypothesis tests, and then use the expected failure probability of hypothesis testing as objective function. Our formalism is unique in that it optimizes field campaigns for maximum confidence in decisions on model choice, binary engineering or management decisions, or questions concerning compliance with environmental performance metrics. It is goal oriented, recognizing that different models, questions, or metrics deserve different treatment. We use a formal Bayesian scheme called PreDIA, which is free of linearization, and can handle arbitrary data types, scientific tasks, and sources of uncertainty (e.g., conceptual, physical, (geo)statistical, measurement errors). This reduces the bias due to possibly subjective assumptions prior to data collection and improves the chances of successful field campaigns even under conditions of model uncertainty. We illustrate our approach on two instructive examples from stochastic hydrogeology with increasing complexity.

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Section: Methodsmentioning

confidence: 99%

Section: Preposterior Stage and Reliability Of A Designmentioning

confidence: 99%

Section: A1 Conditional Simulation and Bayesian Inferencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…This task calls for nonlinear Bayesian inference schemes such as PreDIA [Leube et al, 2012] (see also sections 4.3 and Ax).…”

Section: Hypothesis-driven Optimal Designmentioning

confidence: 99%

See 3 more Smart Citations

A hypothesis‐driven approach to optimize field campaigns

Nowak¹,

Rubin²,

Barros³

2012

Water Resources Research

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Coupling self‐organizing maps with a Naïve Bayesian classifier: Stream classification studies using multiple assessment data

Fytilis

Rizzo

2013

Water Resources Research

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Organizing or clustering data into natural groups is one of the most fundamental aspects of understanding and mining information. The recent explosion in sensor networks and data storage associated with hydrological monitoring has created a huge potential for automating data analysis and classification of large, high‐dimensional data sets. In this work, we develop a new classification tool that couples a Naïve Bayesian classifier with a neural network clustering algorithm (i.e., Kohonen Self‐Organizing Map (SOM)). The combined Bayesian‐SOM algorithm reduces classification error by leveraging the Bayesian's ability to accommodate parameter uncertainty with the SOM's ability to reduce high‐dimensional data to lower dimensions. The resulting algorithm is data‐driven, nonparametric and is as computationally efficient as a Naïve Bayesian classifier due to its parallel architecture. We apply, evaluate and test the Bayesian‐SOM network using two real‐world hydrological data sets. The first uses genetic data to classify the state of disease in native fish populations in the upper Madison River, MT, USA. The second uses stream geomorphic and water quality data measured at ∼2500 Vermont stream reaches to predict habitat conditions. The new classification tool has substantial benefits over traditional classification methods due to its ability to dynamically update prior information, assess the uncertainty/confidence of the posterior probability values, and visualize both the input data and resulting probabilistic clusters onto two‐dimensional maps to better assess nonlinear mappings between the two.

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A method for implementing Dirichlet and third-type boundary conditions in PTRW simulations

Koch

Nowak

2014

Water Resour. Res.

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We present an efficient and accurate numerical method for implementing Dirichlet boundary conditions in particle tracking random walk (PTRW) simulations of advective-dispersive transport. This is a challenge, because defining concentrations for Dirichlet boundary conditions requires invoking control volumes of some kind, which are not natural to the Lagrangian-based PTRW concept. Our method performs a Galerkin projection of PTRW-based particle densities onto control volumes that discretize the boundary. Thus, we obtain concentration values at the boundary condition and can control the particle release rates such that the prescribed boundary values are met. This allows for complex-shaped internal and external boundaries, where concentration values are fixed to prescribed values. Third-type boundary conditions can be addressed as well. We test and illustrate the properties and behavior of our method in a series of test cases. The results are benchmarked against the conceptually related semianalytical method MASST (multiple analytical source superposition technique) and to those of a finite element method (FEM). While MASST is restricted to uniform velocity fields due to the underlying analytical solutions, FEM is limited in heterogeneous velocity fields at large Peclet numbers by numerical dispersion in the feasible discretization range. The results demonstrate that our proposed method performs better than the other methods in both regimes.

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Bayesian assessment of the expected data impact on prediction confidence in optimal sampling design

Cited by 69 publications

References 71 publications

A hypothesis‐driven approach to optimize field campaigns

A hypothesis‐driven approach to optimize field campaigns

Coupling self‐organizing maps with a Naïve Bayesian classifier: Stream classification studies using multiple assessment data

A method for implementing Dirichlet and third-type boundary conditions in PTRW simulations

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