Maximum Weighted Log-Likelihood Estimation for Parameterization Selection Uncertaintyby Frank T-C. Tsai, (M.ASCE),
Abstract: Hydraulic conductivity identification remains a challenging inverse problem in groundwater modeling because of inherent non-uniqueness and lack of flexibility in parameterization methods. This study introduces the maximum weighted log-likelihood estimation (MWLLE) with multiple generalized parameterization (GP)methods to identify hydraulic conductivity and to address non-uniqueness and inflexibility problems in parameterization. A scaling factor to Bayesian information criterion (BIC) is suggested to obtain reasonable parameterization weights for MWLLE and model averaging methods. The scaling factor is a statistical parameter relating to a desired significance level in Occam's window and the variance of the error chi-square distribution. The methodology is demonstrated using a case study in the Alamitos Barrier Project (ABP), California, to identify the hydraulic conductivity field. The averaged hydraulic conductivity and its total conditional variances are obtained by model averaging. The parameter variability and uncertainty are described by the total conditional variances, which include the conditional variances from individual parameterization methods and conditional variances between parameterization methods. The results show that the use of the scaling factor is necessary to avoid a dominant parameterization method in MWLLE. It is concluded that estimation uncertainty increases by including many parameterization methods, but risks are reduced by avoiding overconfidence in one parameterization method.
Subject Headings: Parameters (statistics) | Uncertainty principles | Hydraulic conductivity | Hydraulic models | Fouling | Errors (statistics) | Field tests | Case studies | North America | California | United States
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