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Robust inferential methods for spatio-temporal data in the presence of outliers
Mukangango, Juliette
Mukangango, Juliette
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2024
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The analysis of spatial data primarily focuses on the covariance structure and its parameters, which are typically unknown and require estimation through maximum likelihood (ML) method. However, the presence of outliers, noise, and non-stationary spatial patterns can significantly impact the ML estimators of covariance parameters and associated uncertainties, leading to inaccurate predictions and compromised confidence intervals. Chapters 2 and 3 introduce robust methodologies designed to provide accurate covariance parameter estimates in the presence of outliers without compromising data integrity. The proposed methodologies involve the application of Huber function and a smooth approximation to the Huber function, known as the pseudo-Huber. The Huber function is furthermore used to address limitations of the conventional quadratic loss functions used in the optimization process. Through an intensive numerical study, we observed that the robust estimates closely approximate true values even in the presence of outliers. Chapter \ref{03-Journal-Chapter} presents a novel approach to evaluating operational hydrologic forecasts, as part of the broader initiative of the Cooperative Institute for Research to Operations in Hydrology (CIROH). Our study focuses on assessing the quality of meteorological inputs, including surface precipitation and minimum and maximum temperature from various forcing datasets, to estimate hydrologic variables such as streamflow and snow water equivalent (SWE). By using long short-term memory (LSTM) networks via the Neural-Hydrology library, we perform an extensive analysis over basins across the continental US and snow telemetry sites located in remote, high-elevation, mountain watersheds in the western US. Through these efforts, this research contributes to the advancement of spatial data analysis by providing practitioners with more reliable tools for modeling and predicting spatial phenomena in the presence of outliers and non-stationary spatial patterns. Additionally, this research advances our understanding of hydrologic forecasting capabilities and informing evidence-based decision-making in water resource management.
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