18.650: Fundamentals of Statistics

We learned about the fundamentals of statistics :p

Really though, this was a fun class, I enjoyed it and learned a lot!

From the course catalog: A rapid introduction to the theoretical foundations of statistical methods that are useful in many applications. Covers a broad range of topics in a short amount of time with the goal of providing a rigorous and cohesive understanding of the modern statistical landscape. Mathematical language is used for intuition and basic derivations but not proofs. Main topics include: parametric estimation, confidence intervals, hypothesis testing, Bayesian inference, and linear and logistic regression. Additional topics include causal inference, nonparametric estimation, and classification.

Cheatsheets

Table of Contents

Part 1: Probability and Basics of Statistics

  • Probability Review
  • Lecture 1: Logistics, Introduction, Statistical Pipeline
  • Lecture 2: Descriptive Statistics, OpenIntro Statistics Plots
  • Lecture 3: Convergence of RVs in Probability/Distribution
  • Lecture 4: Gaussian Distribution Review
  • Recitation 1A: Gaussian Standardization, Convergence of RVs
  • Lecture 5: Working With Multivariate Distributions
  • Lecture 6: Multivariate Limit Theorems / Delta Method, Pset 1 Review
  • Lecture 7: Models and Point Estimation
  • Lecture 8: Estimator Properties and Confidence Intervals (CIs)
  • Recitation 1B: Multivariate RVs, Parameter Estimation / MSE
  • Midterm 1 Review: Review and debrief
  • Midterm 1 Cheatsheet

Part 2: Statistical Methods

  • Lecture 9: CI Review, Parameters of Interest, Estimating Parameters
  • Lecture 10: MLE (Maximum Likelihood Estimator), KL Divergence, Fisher Information
  • Lecture 11: MLE Review / Solution Algorithms, Mixtures
  • Lecture 12: EM (Expectation-Maximization) Algorithm for Mixtures
  • Lecture 13: Method of Moments, The Bootstrap
  • Recitation 1C: MLE / Fisher Information, Method of Moments, EM
  • Lecture 14: Bootstrap Properties, Bootstrap CIs

Part 3: Hypothesis Testing

  • Lecture 15: Hypothesis Testing Definitions
  • Lecture 16: Wald Test
  • Midterm 2 Review: Review and debrief
  • Midterm 2 Cheatsheet
  • Lecture 17: p-values
  • Lecture 18: Chi-squared, Pearson’s Goodness of Fit Test, X² Test for Independence, Degrees of Freedom
  • Lecture 19: Nonparametric Tests, Kolmogorov-Smirnov/Two-sample, Kolmogorov-Lilliefors, Permutation Test Intro
  • Lecture 20: Permutation Test, Multiple Hypothesis Tests, Bonferroni Correction, Benjamini-Hochberg (BH) Method

Part 4: Bayesian Inference

  • Lecture 21: Student’s t-distribution, t-test, Frequentist vs. Bayesian, Prior and Posterior
  • Lecture 22: Bayes Estimator, MAP (Maximum A Posteriori), Markov Chain Monte Carlo, Credible Interval

Part 5: Regression

  • Lecture 23: Linear Regression (Formal Specification/Derivation)
  • Lecture 24: Linear Regression Parameter Distributions
  • Lecture 25: Logistic Regression (Binary and Multi-class)
  • Lecture 26: Model Selection, R², AIC/BIC (Akaike/Bayesian Information Criteria), Greedy Forward/Backward, Lasso Method
  • Midterm 3 Review: Review and debrief
  • Midterm 3 Cheatsheet

Part 6: Advanced Topics

  • Lecture 27: Survival Analysis, Kaplan-Meier Estimator, Cox Proportional Hazards
  • Lecture 28: Causal Inference, Counterfactuals, RCTs, Propensity Scores
  • Lecture 29: Nonparametric Curve Estimation with Regression and Histograms, MISE (Mean Integrated Squared Error)
  • Lecture 30: Cross-validation, Kernels/KDE (Kernel Density Estimator), Regressogram, Nadaraya-Watson Estimator
  • Lecture 31: Survey Sampling Methods, Horvitz-Thompson/Hajek Estimators
  • Lecture 32: Bayes Classifier
  • Lecture 33: Data Visualization, Dimensionality Reduction, PCA (Principal Component Analysis), MDS (Multidimensional Scaling), SNE/t-SNE (Stochastic Neighbor Embedding)
  • Final Cheatsheet
Last updated: 22 May 2025

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