MIT 18.650

Fundamentals of Statistics

§ Section 1: Random Variables

Lecture 7: Models and Estimators
- § Models
- § Estimators
Lecture 8: Confidence Intervals
- § Asymptotic Normality
- § Confidence Intervals
Lecture 9: Introducing the MLE
- § Types of Parameters, Identifiability
- § Defining the Maximum Likelihood Estimator (MLE)
Lecture 10: Consistency of the MLE
- § Kullback-Leibler (KL) Divergence
- § MLE Consistency
Lecture 11: MLE Asymptotic Normality
Lecture 12: The EM Algorithm
Lecture 13: Method of Moments and Bootstrap
Lecture 14: Bootstrap Properties and Constructing CIs

Lecture 15: Introduction to Hypothesis Testing
- § Hypothesis Testing
- § Error Types
Lecture 16: The Wald Test
Lecture 17: $p$ -Values
Lecture 18: Goodness of Fit and T Tests
Lecture 19: Non-parametric Tests
Lecture 20: Permutation Test and Multiple Hypothesis Testing

Lecture 21: Bayesian Inference I
Lecture 22: Bayesian Inference II
- § Computing the Bayes Estimator and MAP
- § Gaussian Conjugate Priors

Lecture 23: Linear Regression I
Lecture 24: Linear Regression II
Lecture 25: Logistic Regression
- § MLE for Logistic Regression
- § Multiclass Classification