Natural hazard assessments provide the foundation for the planning, design, and analysis of engineered systems. However, natural hazard assessments are subject to uncertainties due to natural variability and our imperfect understanding of hazardous processes. Underestimation or poor characterization of uncertainty can lead to incorrect or misleading estimates of hazards. This dissertation includes two main research thrusts focused on sources of uncertainty in probabilistic hazard assessments of coastal and precipitation hazards. The first thrust considers uncertainty arising from the application of machine learning (ML) methods, and the second thrust focuses on uncertainty arising from statistical modeling choices. To support the first research thrust, two studies are performed to explore and characterize epistemic uncertainties associated with evaluating the performance of ML models employed in natural hazard estimation. First, a comprehensive framework is developed to investigate and compare the behavior of multiple ML models used to predict storm surge hazards. This is achieved by assessing their performance in predicting large target response quantities, identifying systematic trends in errors, and leveraging conventional performance metrics. In the second study, ML models are developed to temporally downscale climate model projection time-series from 3-hour to 15-minute time-steps. The assessment framework previously used for storm surge hazards is applied, with the addition of the strategic assessment of input/output relationships using response functions and consideration of composite error metrics. Under the second research thrust, two studies are conducted to demonstrate processes and strategies for investigating and characterizing epistemic uncertainties associated with statistical modeling choices in precipitation frequency analysis under current and future climate conditions. First, a comparative assessment of sources of uncertainty is performed for at-site and regional frequency analysis considering a case study of Ellicott City, Maryland, under current climatic conditions. Then, a more extensive study investigates and contextualizes the relative importance of epistemic uncertainties associated with statistical modeling choices and climate model selection on intensity duration frequency curves for the State of Maryland under current and future climate. The insights obtained by this dissertation can inform the decision-making through providing more robust estimation and understanding of hazards and the associated uncertainty.