18.6501x Fundamentals of Statistics

General

• All of Statistics by Larry Wasserman (course-recommended supplementary text, free download from publisher)

Unit 1 Introduction to statistics

Lecture 1: What is statistics

Lecture 2: Probability Redux

Unit 2 Foundation of Inference

Lecture 3: Parametric Statistical Models

Lecture 4: Parametric Estimation and Confidence Intervals

• A Short Intro to Confidence Intervals by Sean Kross
• Confidence Interval Interpretations and Misunderstandings by Fred Schenkelberg

Lecture 5: Delta Method and Confidence Intervals

Lecture 6: Introduction to Hypothesis Testing, and Type 1 and Type 2 Errors

Lecture 7: Hypothesis Testing (Continued): Levels and P-values

Unit 3 Methods of Estimation

Lecture 8: Distance measures between distributions

Lecture 9: Introduction to Maximum Likelihood Estimation

• Gradient, Hessian, and Jacobian by Glyn A. Holton

Lecture 10: Consistency of MLE, Covariance Matrices, and Multivariate Statistics

Lecture 11: Fisher Information, Asymptotic Normality of MLE; Method of Moments

Lecture 12: M-Estimation

Recitation 9: (Review) Mean Squared Error

Recitation 10: (Review) Multivariate Gaussian

Recitation 11: (Review) Method of Moments

Unit 4 Hypothesis testing

Lecture 13: Chi Squared Distribution, T-Test

Lecture 14: Wald's Test, Likelihood Ratio Test, and Implicit Hypothesis Test

• Power of a hypothesis test (large sample version) by melbapplets

Lecture 15: Goodness of Fit Test for Discrete Distributions

Recitation 15: Chi Squared Goodness of Fit Test

• The Statistics Tutor's Quick Guide to Commonly Used Statistical Tests by statstutor

Lecture 16: Goodness of Fit Tests Continued: Kolmogorov-Smirnov test, Kolmogorov-Lilliefors test, Quantile-Quantile Plots

• A Q-Q Plot Dissection Kit by Sean Kross

Unit 5 Bayesian statistics

Lecture 17: Introduction to Bayesian Statistics

• Beta Distribution — Intuition, Examples, and Derivation by Aerin Kim
• The Beta distribution in 12 minutes! by Luis Serrano
• Beta Distribution PDF Grapher by Peter Rosenmai
• Conjugate Prior Explained by Aerin Kim
• Bayesian Updating: Continuous Priors by MIT OCW (18.05 Spring 2014)

Recitation 20: Calculating Bayes Posteriors

Lecture 18: Jeffreys Prior and Bayesian Confidence Interval

Recitation 21: Multinomial Bayesian Estimation

Recitation 22: Jeffreys Prior

(Optional) Recitation: Jeffreys Prior in Higher Dimension

Unit 6 Linear Regression

Lecture 19: Linear Regression 1

Lecture 20: Linear Regression 2

• Multiple Linear Regression from Scratch in Numpy by Dario Radečić

Recitation 23: Hypothesis Test for Linear Regression

Recitation 24: Multiple Hypothesis Testing and Bonferroni Correction

Recitation 25: Ridge Regression

Unit 7 Generalized Linear Models

Lecture 21: Introduction to Generalized Linear Models; Exponential Families

• Exponential family "Table of distributions" by Wikipedia
• The Exponential Family by David Blei (especially the last page "The Big Picture"

Lecture 22: GLM: Link Functions and the Canonical Link Function

Recitation 26: Poisson and Gamma Generalized Linear Models

Recitation 27: Hypothesis Test for Logistic regression

(Optional) Unit 8 Principal component analysis

(Optional) Lecture 23: Principal Component Analysis

(Optional) Recitation 28: Principal Component Regression