Fundamentals of Statistics

18.6501x Fundamentals of Statistics is an MITx course in the MicroMasters Program in Statistics and Data Science. Its purpose is to develop the core ideas of statistics on firm mathematical grounds, starting from the construction of estimators and tests and the analysis of their asymptotic performance. After building the basic tools for parametric models, the course turns to more advanced questions: how suitable a model is for a dataset, how to select variables in linear regression, how to model nonlinear phenomena and how to visualise high-dimensional data. The stated goal is that you leave with the mathematical principles that link statistical methods together, not just a list of techniques.

The learning outcomes cover method of moments and maximum likelihood estimators, confidence intervals and hypothesis testing, goodness-of-fit tests for model selection, prediction with linear, nonlinear and generalised linear models, and principal component analysis. The course is instructor-paced and estimated at 17 weeks. Auditing is free with access to the course materials for the length of the session (MIT's help centre says audit access ends shortly after the session closes), while the $300 certificate track adds graded assignments and exams and an MIT certificate on completion and can count toward the MicroMasters credential. OpenCourseWare's 18.650 Statistics for Applications covers related material without grading.