Foundations of Statistical Inference and Decision Theory

Catalog description

This is an accelerated course providing advanced training in statistical theory for students who have completed an introductory graduate course in statistical inference (e.g., BIOSTAT 704 or equivalent) and seek further preparation for PhD-level study in mathematical statistics. The course emphasizes the development of a rigorous mathematical toolkit for statistical reasoning, including proof techniques, limits and asymptotics, Taylor expansions, convexity, and optimization methods, all applied within statistical contexts. Core topics include multivariate probability and conditioning, modes of convergence and asymptotic theory, likelihood and information, classical optimal estimation, decision-theoretic foundations of inference, and the duality between hypothesis testing and confidence sets. Computational aspects of modern inference are incorporated through likelihood optimization and the EM algorithm. Selected topics in multiple testing and limitations of classical inference in high-dimensional settings are also introduced. Prerequisites: Enrollment in the Master of Biostatistics Program Health AI track, BIOSTAT 704, or permission from the Director of Graduate Studies. Credits 3