Statistics for Applications

18.650 Statistics for Applications is MIT's undergraduate course in mathematical statistics, and the fall 2016 edition taught by Philippe Rigollet is on OpenCourseWare with video of the lectures. It gives the theoretical foundations for statistical methods used in applications, with the aim of understanding the role mathematics plays in developing efficient methods. By the end, students should be able to state a statistical problem mathematically from a real situation, select appropriate methods, and understand their implications and limits. The topics covered are an introduction to statistics, parametric inference, maximum likelihood estimation, the method of moments, parametric hypothesis testing, testing goodness of fit, regression, Bayesian statistics, principal component analysis and generalised linear models; the lecture videos follow this order, with several lectures devoted to each block.

Lecture slides and the assignments are provided alongside the videos. The on-campus grading, listed for reference, was homework, a midterm and a final exam, but the OpenCourseWare version has no grading or deadlines and you work through the material at your own pace. There is no account to create, the content is free under a Creative Commons licence, and no certificate is offered. For a graded version with a paid certificate option, MITx Online's 18.6501x Fundamentals of Statistics covers similar ground.