Abstract.
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. A comprehensive strategy for constructing alternative conceptual-mathematical models of subsurface flow and transport, selecting the best among them, and using them jointly to render optimum predictions under uncertainty has recently been developed by Neuman and Wierenga (2003). This paper describes a key formal element of this much broader and less formal strategy that concerns rendering optimum hydrologic predictions by means of several competing deterministic or stochastic models and assessing their joint predictive uncertainty. The paper proposes a Maximum Likelihood Bayesian Model Averaging (MLBMA) method to accomplish this goal. MLBMA incorporates both site characterization and site monitoring data so as to base the outcome on an optimum combination of prior information (scientific knowledge plus data) and model predictions. A preliminary example based on real data is included in the paper.
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This work was supported by the U.S. Nuclear Regulatory Commission under contract NRC-04–97–056. Special credit is due to Thomas J. Nicholson and Ralph Cady of the USNRC for having conceived and championed this research. I am most grateful to Weihsueh Chiu of the U.S. Environmental Protection Agency for having brought to my attention the extensive work on BMA conducted by the “Seattle school” of statistics at the University of Washington, and for his helpful comments on this paper.
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Neuman, S. Maximum likelihood Bayesian averaging of uncertain model predictions. Stochastic Environmental Research and Risk Assessment 17, 291–305 (2003). https://doi.org/10.1007/s00477-003-0151-7
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DOI: https://doi.org/10.1007/s00477-003-0151-7