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Statistics for Applications (18.650)

4.8(3,200) on MIT OpenCourseWare·450K enrolled
Intermediate 30 hours EnglishFREE
SkillsStatisticsHypothesis testingRegressionEstimationBayesian statisticsStatistical inference

Is this course right for you?

Our take
Worth it if you want the mathematical foundations of statistics, taught rigorously. It is free from MIT, with proofs rather than just formulas.

Good for: mathematically comfortable learners who want rigorous applied statistics.

Skip if: you want a gentle, applied-only course, or you need a certificate.

Philippe Rigollet covers estimation and maximum likelihood, confidence intervals, hypothesis testing (frequentist and Bayesian), and regression at graduate pace. It is the statistics counterpart to MIT's linear algebra course, and the level applied courses like Khan's do not reach.

It is demanding and proof-heavy, so it is the wrong fit if you want a gentle, applied-only course or need a certificate — there is none from the free materials. If you want application over theory, take an applied statistics course instead. The recordings are from 2016, but the mathematics is still relevant.

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About this course

MIT 18.650 is a graduate-level statistics course covering the mathematical foundations of statistical inference: parameter estimation and maximum likelihood, confidence intervals, hypothesis testing (frequentist and Bayesian), linear and logistic regression, and goodness-of-fit tests. Philippe Rigollet teaches it with full mathematical rigor — proofs, not just formulas — at the pace MIT graduate students experience.

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Instructor

PR
Philippe Rigollet
MIT OpenCourseWare instructor
450K+ learners5 courses4.8 instructor rating

Taught by Philippe Rigollet, Professor of Mathematics at MIT, whose research focuses on statistics and machine learning theory.

Frequently asked questions

A fair amount, and it does not hold your hand. MIT lists probability at the level of a first probability course, single-variable calculus, and some linear algebra with vectors and matrices. Without those, the derivations early on will lose you quickly, because the course assumes them as background rather than pausing to reteach — so shore up any gaps before you begin rather than during.

Less than the reputation of an MIT maths course might suggest. It uses mathematical language for intuition and basic derivations rather than long formal proofs, so the emphasis stays on understanding why statistical methods work and when to use them. You will still see real derivation and notation, but the goal is genuine comprehension of the methods, not proving every theorem rigorously from first principles.

No. This is MIT OpenCourseWare, meaning you get the lecture videos, problem sets, and exams as published files, usually with solutions, but there is no enrolment, no autograder, no instructor, and no certificate. It rewards genuine self-discipline: you work the problems yourself and check against the provided answers, which suits motivated self-learners far more than anyone needing external structure or accountability.

They sit at opposite ends. Khan Academy builds statistical intuition gently for beginners, with lots of hand-holding. This is a genuine MIT undergraduate course covering estimation, maximum likelihood, hypothesis testing, regression, and Bayesian methods with real mathematical depth. If the prerequisites above feel shaky, do Khan Academy first — jumping straight here without that grounding tends to end in frustration rather than learning.

The core theory of modern statistics: parametric inference and maximum likelihood estimation, the method of moments, hypothesis testing and goodness of fit, regression, Bayesian statistics, principal component analysis, and generalised linear models. In other words, the mathematical machinery that data science and machine learning quietly depend on — this is the 'why it works' behind the methods you may already be applying elsewhere.
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