HR: 1340h
AN: H13A-0397    [Abstracts]
TI: Estimating Prior Model Probabilities Using an Entropy Principle
AU: * Ye, M
EM: Ming.Ye@dri.edu
AF: Desert Research Institute, University and Community College System of Nevada, 755 E. Flamingro Raod, Las Vegas, NV 89119 United States
AU: Meyer, P D
EM: Philip.Meyer@pnl.gov
AF: Pacific Northwest National Laboratory, 620 SW 5th Ave., Suite 810, Portland, OR 97204 United States
AU: Neuman, S P
EM: neuman@hwr.arizona.edu
AF: Department of Hydrology and Water Resources, The University of Arizona, Tucson, AZ 85721
AU: Pohlmann, K
EM: Karl.Pohlmann@dri.edu
AF: Desert Research Institute, University and Community College System of Nevada, 755 E. Flamingro Raod, Las Vegas, NV 89119 United States
AB: Considering conceptual model uncertainty is an important process in environmental uncertainty/risk analyses. Bayesian Model Averaging (BMA) (Hoeting et al., 1999) and its Maximum Likelihood version, MLBMA, (Neuman, 2003) jointly assess predictive uncertainty of competing alternative models to avoid bias and underestimation of uncertainty caused by relying on one single model. These methods provide posterior distribution (or, equivalently, leading moments) of quantities of interests for decision-making. One important step of these methods is to specify prior probabilities of alternative models for the calculation of posterior model probabilities. This problem, however, has not been satisfactorily resolved and equally likely prior model probabilities are usually accepted as a neutral choice. Ye et al. (2004) have shown that whereas using equally likely prior model probabilities has led to acceptable geostatistical estimates of log air permeability data from fractured unsaturated tuff at the Apache Leap Research Site (ALRS) in Arizona, identifying more accurate prior probabilities can improve these estimates. In this paper we present a new methodology to evaluate prior model probabilities by maximizing Shannon's entropy with restrictions postulated a priori based on model plausibility relationships. It yields optimum prior model probabilities conditional on prior information used to postulate the restrictions. The restrictions and corresponding prior probabilities can be modified as more information becomes available. The proposed method is relatively easy to use in practice as it is generally less difficult for experts to postulate relationships between models than to specify numerical prior model probability values. Log score, mean square prediction error (MSPE) and mean absolute predictive error (MAPE) criteria consistently show that applying our new method to the ALRS data reduces geostatistical estimation errors provided relationships between models are postulated correctly. We illustrate our method further by using it to assess the comparative conceptual uncertainty of five recharge models developed by three independent parties for the Nevada Test Site. Influence of the recharge model uncertainty to predictive uncertainty of the flow model is explored.
DE: 6309 Decision making under uncertainty
DE: 1829 Groundwater hydrology
DE: 1869 Stochastic processes
DE: 1875 Unsaturated zone
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting