This course is an introduction to the ideas and tools of probability: sample spaces, conditioning, Bayes’ Rule, random variables, distributions, expected values and moments, and Markov chains. It’s also a chance to see many interesting examples such as the Birthday Problem, Gambler’s Ruin, St. Petersburg Paradox, and Google PageRank as a Markov Chain.
Stroboscopic image of a coin flip by Andrew Davidhazy, used with permission.
Spring 2007: Stat 211 (Statistical Inference), taught jointly with Carl Morris
This course is a graduate level introduction to inference from likelihoodist, frequentist, Bayesian, and decision analytic points of view.
Spring 2007: Stat 230 (Multivariate Analysis), taught jointly with Carl Morris
This course delves into matrix algebra, the multivariate normal distribution and its offshoots, multilevel and Bayesian models, and techniques such as principal component analysis, factor analysis, canonical correlations, multidimensional scaling, and projection pursuit.
I enjoy teaching, and try hard to make ideas accessible and interesting. I try to find a happy medium between technical details and the big picture. For example, I remember a lecture where a theorem was described in terms of a lighthouse. The professor drew a picture of the lighthouse and spent over half an hour discussing the lighthouse, without writing anything else down on the board. The imaginary lighthouse was more illuminating than the lecture.
At the other extreme, I've attended all too many talks and lectures where the speaker bombards the audience with line after line of messy expressions and complicated notations, presented without motivation or intuition. A good lecture should give both the central intuitions and sufficient detail. I try to keep lectures interactive, both to make them more interesting and to help in finding the right balance.
Before coming to Harvard, I was a calculus instructor twice, and a teaching assistant for many courses including multivariable calculus, differential equations, linear algebra and matrix theory, real analysis, combinatorics, and probability.
Harvard Courses