Spatial Statistics

Undergraduate

This course provides a comprehensive introduction to spatial statistics, focusing on statistical modeling and inference for data exhibiting spatial dependence. The course covers the major classes of spatial data, including geostatistical (continuous-domain), areal (lattice), and spatial point pattern data, and develops modeling frameworks tailored to each setting. Core topics include covariance functions and variograms, Gaussian random fields, kriging and spatial prediction, spatial regression models, conditional and simultaneous autoregressive (CAR/SAR) models for areal data, and Poisson and Cox processes for point patterns. Emphasis is placed on model construction, interpretation, and derivation of key estimators and predictors, with attention to both likelihood-based and hierarchical modeling approaches. Students will learn to assess model assumptions, quantify uncertainty, and address practical challenges such as spatial confounding and computational scalability for large datasets. The course also introduces modern developments connecting spatial statistics with machine learning, including Gaussian process methods and scalable approximations. Through theoretical development, problem sets, and a data-driven project, students will gain the skills necessary to formulate, implement, and evaluate spatial statistical models in scientific, environmental, biomedical, and social science applications. Probability theory at the level of S&DS 2410 /5410, statistical inference at the level of S&DS 2420 /5420, linear algebra at the level of MATH 2250 or 2260 , and experience with computing and data analysis in common programming languages such as R and Python. Familiarity with linear models (e.g., S&DS 3120 /6120) and Bayesian methods (e.g., S&DS 3540 /5540) is helpful but not required. QR TTh 2:35pm-3:50pm