A Bayesian View of Uncertainty Quantication and Reduction
Rubin, Yoram
UC Berkeley
2019
UC Berkeley
2019
Groundwater plays a crucial role in our water resources. To counteract the growing demand and depletion of groundwater resources and devise sustainable management plans, a wide range of models have been applied to make estimates/predictions of various hydrogeologic responses. However, uncertainty arises in all modeling applications, and the quantification/reduction of modeling uncertainty has been a challenge for all hydrogeologists, especially at unsampled locations. The main challenge posed at unsampled locations is the lack of in-situ data, forcing us to search for alternative sources of information, and systematically assimilate the said information in order to obtain conditioned estimates of hydrologic responses.To that end, the primary objective of this dissertation is the advancement of stochastic modeling approaches targeting at unsampled locations. Under the context of the primary objective, we propose three different stochastic modeling approaches that are designed to assimilate three alternative sources of information, respectively.First, we propose the Rapid Impact Modeling (RIM) approach to efficiently assimilate in-situ soft data (i.e., in-situ data that are related to the target response via transfer functions) for obtaining conditioned estimates. RIM improves upon the existing approximate Bayesian computation approaches by (1) bypassing the estimation of posterior distributions of model parameters, thus reducing the computation burden, and (2) relaxing the need to reduce data into summary statistics, thus avoiding losing information.To demonstrate the power of RIM, we address the challenge of data scarcity against the backdrop of a 7