TY - JOUR
T1 - Bayesian analysis of data-worth considering model and parameter uncertainties
AU - Neuman, Shlomo P.
AU - Xue, Liang
AU - Ye, Ming
AU - Lu, Dan
N1 - Funding Information:
This research was 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. The third and fourth authors were supported in part by NSF-EAR Grant 0911074 and DOE-ERSP Grant DE-SC0002687 .
PY - 2012/2
Y1 - 2012/2
N2 - The rational management of water resource systems requires an understanding of their response to existing and planned schemes of exploitation, pollution prevention and/or remediation. Such understanding requires the collection of data to help characterize the system and monitor its response to existing and future stresses. It also requires incorporating such data in models of system makeup, water flow and contaminant transport. As the collection of subsurface characterization and monitoring data is costly, it is imperative that the design of corresponding data collection schemes be cost-effective, i.e., that the expected benefit of new information exceed its cost. A major benefit of new data is its potential to help improve one's understanding of the system, in large part through a reduction in model predictive uncertainty and corresponding risk of failure. Traditionally, value-of-information or data-worth analyses have relied on a single conceptual-mathematical model of site hydrology with prescribed parameters. Yet there is a growing recognition that ignoring model and parameter uncertainties render model predictions prone to statistical bias and underestimation of uncertainty. This has led to a recent emphasis on conducting hydrologic analyses and rendering corresponding predictions by means of multiple models. We describe a corresponding approach to data-worth analyses within a Bayesian model averaging (BMA) framework. We focus on a maximum likelihood version (MLBMA) of BMA which (a) is compatible with both deterministic and stochastic models, (b) admits but does not require prior information about the parameters, (c) is consistent with modern statistical methods of hydrologic model calibration, (d) allows approximating lead predictive moments of any model by linearization, and (e) updates model posterior probabilities as well as parameter estimates on the basis of potential new data both before and after such data become actually available. We describe both the BMA and MLBMA versions theoretically and implement MLBMA computationally on a synthetic example with and without linearization.
AB - The rational management of water resource systems requires an understanding of their response to existing and planned schemes of exploitation, pollution prevention and/or remediation. Such understanding requires the collection of data to help characterize the system and monitor its response to existing and future stresses. It also requires incorporating such data in models of system makeup, water flow and contaminant transport. As the collection of subsurface characterization and monitoring data is costly, it is imperative that the design of corresponding data collection schemes be cost-effective, i.e., that the expected benefit of new information exceed its cost. A major benefit of new data is its potential to help improve one's understanding of the system, in large part through a reduction in model predictive uncertainty and corresponding risk of failure. Traditionally, value-of-information or data-worth analyses have relied on a single conceptual-mathematical model of site hydrology with prescribed parameters. Yet there is a growing recognition that ignoring model and parameter uncertainties render model predictions prone to statistical bias and underestimation of uncertainty. This has led to a recent emphasis on conducting hydrologic analyses and rendering corresponding predictions by means of multiple models. We describe a corresponding approach to data-worth analyses within a Bayesian model averaging (BMA) framework. We focus on a maximum likelihood version (MLBMA) of BMA which (a) is compatible with both deterministic and stochastic models, (b) admits but does not require prior information about the parameters, (c) is consistent with modern statistical methods of hydrologic model calibration, (d) allows approximating lead predictive moments of any model by linearization, and (e) updates model posterior probabilities as well as parameter estimates on the basis of potential new data both before and after such data become actually available. We describe both the BMA and MLBMA versions theoretically and implement MLBMA computationally on a synthetic example with and without linearization.
KW - Bayesian model averaging
KW - Data worth
KW - Model uncertainty
KW - Parameter uncertainty
KW - Value of information
UR - http://www.scopus.com/inward/record.url?scp=84855222661&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84855222661&partnerID=8YFLogxK
U2 - 10.1016/j.advwatres.2011.02.007
DO - 10.1016/j.advwatres.2011.02.007
M3 - Article
AN - SCOPUS:84855222661
SN - 0309-1708
VL - 36
SP - 75
EP - 85
JO - Advances in Water Resources
JF - Advances in Water Resources
ER -