Spatial Prediction Under Uncertainty: Methodological and Computational Advances in Bayesian Maximum Entropy

Environmental decisions such as infrastructure design, water management, and snow load estimation depend on spatial data that are often incomplete or uncertain. In many cases, measurements are not exact values but ranges, reflecting limitations in data collection methods. Traditional mapping techniques typically simplify these uncertain measurements, which can lead to less accurate predictions. This dissertation introduces improved statistical tools for making spatial predictions when data are uncertain or partially known. By utilizing a framework called Bayesian Maximum Entropy (BME), this research demonstrates how exact measurements and range-based data can be combined in a mathematically consistent way. The work demonstrates that this approach produces more accurate and reliable predictions than traditional methods, especially when the data are skewed or highly variable. In addition, a new extension called Quantile-based BME is developed to better represent uncertainty within interval data, further improving predictive performance. To make these methods widely accessible, this dissertation also introduces a free, open-source software package in R that allows researchers and practitioners to apply these advanced techniques in real-world settings. Together, these contributions provide more reliable tools for environmental mapping and risk assessment, supporting better decision-making in fields such as snow load design, hydrology, and climate analysis.