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