This Faculty Early Career Development Program (CAREER) grant will contribute to advancing the nation’s leadership in data science by establishing new statistical methods for analyzing data that take the form of probability distributions rather than single numbers. In many modern scientific and engineering applications, including single cell biology, biotechnology, and advanced manufacturing, data are naturally represented by probability distributions, such as histograms or probability functions, describing variability within measurements. However, most current analytical methods reduce this rich distributional information to simple summary statistics, such as averages, thereby discarding valuable information and potentially limiting scientific insights. This project addresses the fundamental challenge of building rigorous statistical tools capable of directly modeling and drawing inferences from distribution-valued data. By preserving the full structure of the data, these methods will enable researchers and practitioners to uncover complex patterns and relationships that existing approaches may miss. The resulting tools have the potential to accelerate discoveries in areas such as perioperative medicine, biomarker identification for diagnosis and drug development, thereby strengthening the global competitiveness of the nation in data science and artificial intelligence. The educational components will provide training opportunities for undergraduate students and high school students in engineering statistics and biotechnology, while preparing graduate students to work in this emerging interdisciplinary field. This project will also engage the broader community through open-source software, accessible educational materials, and data challenge competitions. These efforts aim to broaden participation in science, technology and engineering, and support the development of a competitive workforce equipped with next-generation data analysis skills. This research will e