TY - JOUR
T1 - Multimodel Bayesian analysis of data-worth applied to unsaturated fractured tuffs
AU - Lu, Dan
AU - Ye, Ming
AU - Neuman, Shlomo P.
AU - Xue, Liang
N1 - Funding Information:
The first and second authors were supported in part by NSF-EAR Grant 0911074 and DOE-ERSP Grant DE-SC0002687 . The second author was also supported by the COFRS project of the Florida State University. The third and fourth authors were supported in part through a contract between the University of Arizona and Vanderbilt University under the Consortium for Risk Evaluation with Stakeholder Participation (CRESP) III, funded by the US Department of Energy.
PY - 2012/1
Y1 - 2012/1
N2 - To manage water resource and environmental systems effectively requires suitable data. The worth of collecting such data depends on their potential benefit and cost, including the expected cost (risk) of failing to take an appropriate decision. Evaluating this risk calls for a probabilistic approach to data-worth assessment. Recently we [39] developed a multimodel approach to optimum value-of-information or data-worth analysis based on model averaging within a maximum likelihood Bayesian framework. Adopting a two-dimensional synthetic example, we implemented our approach using Monte Carlo (MC) simulations with and without lead order approximations, finding that the former approach was almost equally accurate but computationally more efficient. Here we apply our methodology to pneumatic permeability data from vertical and inclined boreholes drilled into unsaturated fractured tuff near Superior, Arizona. In an attempt to improve computational efficiency, we introduce three new approximations that require less computational effort and compare results with those obtained by the original Monte Carlo method. The first approximation disregards uncertainty in model parameter estimates, the second does so for estimates of potential new data, and the third disregards both uncertainties. We find that only the first approximation yields reliable quantitative assessments of reductions in predictive uncertainty brought about by the collection of new data. We conclude that, whereas parameter uncertainty may sometimes be disregarded for purposes of analyzing data worth, the same does not generally apply to uncertainty in estimates of potential new data.
AB - To manage water resource and environmental systems effectively requires suitable data. The worth of collecting such data depends on their potential benefit and cost, including the expected cost (risk) of failing to take an appropriate decision. Evaluating this risk calls for a probabilistic approach to data-worth assessment. Recently we [39] developed a multimodel approach to optimum value-of-information or data-worth analysis based on model averaging within a maximum likelihood Bayesian framework. Adopting a two-dimensional synthetic example, we implemented our approach using Monte Carlo (MC) simulations with and without lead order approximations, finding that the former approach was almost equally accurate but computationally more efficient. Here we apply our methodology to pneumatic permeability data from vertical and inclined boreholes drilled into unsaturated fractured tuff near Superior, Arizona. In an attempt to improve computational efficiency, we introduce three new approximations that require less computational effort and compare results with those obtained by the original Monte Carlo method. The first approximation disregards uncertainty in model parameter estimates, the second does so for estimates of potential new data, and the third disregards both uncertainties. We find that only the first approximation yields reliable quantitative assessments of reductions in predictive uncertainty brought about by the collection of new data. We conclude that, whereas parameter uncertainty may sometimes be disregarded for purposes of analyzing data worth, the same does not generally apply to uncertainty in estimates of potential new data.
KW - Data uncertainty
KW - Data worth
KW - Model uncertainty
KW - Parameter uncertainty
KW - Uncertainty reduction
KW - Value of information
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U2 - 10.1016/j.advwatres.2011.10.007
DO - 10.1016/j.advwatres.2011.10.007
M3 - Article
AN - SCOPUS:82355187637
SN - 0309-1708
VL - 35
SP - 69
EP - 82
JO - Advances in Water Resources
JF - Advances in Water Resources
ER -