In the exploration and planning phases of geothermal energy projects, data are often limited and imprecise. As a result, the uncertainty in derived geothermal variables can be large. To address those problems, this thesis develops exploratory spatial data analysis procedures to identify discordant observations in datasets of derived geothermal variables, and a stochastic framework to propagate uncertainty through geothermal resource assessment and geothermal reservoir models. The resulting uncertainty distributions should inform project decisions and guide prioritization of additional data collection and modeling. This research is applied to Appalachian Basin geothermal resource characterization, and to assess the feasibility of using geothermal reservoirs to meet direct-use heating objectives for the Cornell University campus in Ithaca, NY. Exploratory spatial data analysis (ESDA) can identify discordant observations in datasets derived from low-quality bottom-hole temperature (BHT) measurements taken during well drilling. Spatial regressions that characterize geothermal resources commonly employ such datasets. A local median deviation procedure informs a minimum depth for BHT measurements to represent conduction-dominated heat transfer for the Appalachian Basin. A subsequent local spatial outlier identification procedure detects discordant observations using asymmetric boxplots. Using ESDA procedures and removing discordant observations significantly reduced and stabilized semi-variance estimates of spatial autocorrelations. Striking differences are found in spatial autocorrelation functions employed for regressions in separate geologic regions. A stochastic framework supports uncertainty and sensitivity analysis of geothermal resource assessment models. Assessments require transforming BHT measurements into heat flows at well sites, and employing spatial regression to estimate heat flow across the region. Uncertainties in geologic properties and predicted surface heat flows are propagated through models to obtain uncertainty distributions of temperature-depth profiles across the Appalachian Basin, and distributions of thermal energy within potential geothermal reservoirs. Sensitivity analyses reveal variables whose uncertainties contribute most to thermal energy uncertainty; the results are a function of a reservoir’s spatial location and the depth of available temperature data. Many geologic variables may be assigned regional values with large uncertainties with little impact on the thermal energy uncertainty. Stochastic evaluation of geothermal reservoir production models transforms geothermal resource assessment uncertainties into decision-relevant information for project planning. Several reservoir flow geometries and production scenarios are compared using analytical and numerical reservoir models. The analysis generates the joint probability over time that a production scenario achieves specified heating objectives. Uncertainties in reservoir flow geometry provided a wide range of possible useful lifetimes for target geothermal reservoirs.