Foundations of Mathematical Statistics
A rigorous mathematical foundation for advanced study in biostatistics theory, covering concepts in real analysis, functional analysis, and measure-theoretic probability. Designed to strengthen students' mathematical fluency and their ability to construct precise and rigorous mathematical arguments, the course begins with fundamentals of real analysis, including limits, continuity, differentiation, and integration in Euclidean spaces. It then turns to measure-theoretic probability, introducing sigma-algebras, measures and signed measures, Lebesgue integration, expectations, the Radon–Nikodym derivative, conditioning, and modes of convergence for random variables as well as key topics in functional analysis and functional derivatives.
Topics
- •Build a solid foundation in analysis, including key concepts such as Banach and Hilbert spaces, orthogonality, projections, functional derivatives, and bounded linear operators between normed spaces •Gain a rigorous understanding of measure-theoretic probability and analyze modes of convergence for real-valued random variables, as well as weak convergence in general metric spaces •Develop the ability to construct and communicate precise and rigorous mathematical arguments and proofs, particularly in the context of statistical theory •Connect the mathematical concepts learned in this course to theory in semiparametric efficiency and asymptotic statistics
Official catalogue course objectives and student learning outcomes
Sources
- Course catalogue ↗2026-2027