This course introduces probability theory and thus serves as a basis for courses in statistical inference (572-574) and game theory (575-576). We will begin with an axiomatic treatment of the standard model of probability and develop an understanding of random variables, distributions, and expectations/moments. The development of conditional expectations and distributions will serve as a framework to think about learning. We will then cover hypothesis testing and asymptotic theory from the classical perspective as well as the Bayesian approach to decision-theory. Connections between these historically significant approaches will be traced out. The class will end with introductions to regression from the perspective of projection and optimization. If time permits we will also introduce Maximum likelihood estimation. I precepted this course for Adam Meirowitz in the fall of 2012.

Course Syllabus