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Probability & Statistics

From describing data to Radon-Nikodym derivatives: probability, random variables, limit theorems, estimation, hypothesis testing, regression, Bayesian inference, stochastic processes, information theory and Monte Carlo. Teaches the misuse of each tool as carefully as the tool. Assumes basic calculus.

intermediate Free statisticsprobabilitydata-sciencepython
🎬 67 videos ⚡ 67 exercises · 928 min total
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12 modules · 67 lessons
0. Foundations of Probability 7 lessons · 74 min
  1. 1 Describing data 🎬 13 min
  2. 2 What is probability? 🎬 12 min
  3. 3 Sample spaces, events and the axioms 🎬 10 min
  4. 4 Combinatorics: permutations, combinations, inclusion–exclusion 🎬 10 min
  5. 5 Conditional probability and Bayes' theorem 🎬 10 min
  6. 6 Independence of events 🎬 10 min
  7. 7 The law of total probability 🎬 9 min
1. Random Variables 7 lessons · 95 min
  1. 8 Discrete random variables and the PMF 🎬 13 min
  2. 9 Continuous random variables, PDF and CDF 🎬 12 min
  3. 10 Expectation, variance and standard deviation 🎬 12 min
  4. 11 Moments and moment generating functions 🎬 12 min
  5. 12 Characteristic functions 🎬 13 min
  6. 13 Common discrete distributions 🎬 15 min
  7. 14 Common continuous distributions 🎬 18 min
2. Multivariate Distributions 7 lessons · 88 min
  1. 15 Joint, marginal and conditional distributions 🎬 13 min
  2. 16 Independence of random variables 🎬 12 min
  3. 17 Covariance and correlation 🎬 13 min
  4. 18 Transformations and the Jacobian method 🎬 12 min
  5. 19 Order statistics 🎬 11 min
  6. 20 The multivariate Normal 🎬 14 min
  7. 21 Copulas (intro) 🎬 13 min
3. Limit Theorems 4 lessons · 48 min
  1. 22 Modes of convergence 🎬 13 min
  2. 23 The law of large numbers 🎬 11 min
  3. 24 The central limit theorem 🎬 12 min
  4. 25 The delta method and Slutsky's theorem 🎬 12 min
4. Statistical Inference — Estimation 7 lessons · 91 min
  1. 26 Point estimation: bias, variance and MSE 🎬 13 min
  2. 27 The method of moments 🎬 12 min
  3. 28 Maximum likelihood estimation 🎬 13 min
  4. 29 Sufficiency and the factorization theorem 🎬 13 min
  5. 30 Fisher information and the Cramér–Rao bound 🎬 13 min
  6. 31 Confidence intervals 🎬 14 min
  7. 32 Consistency and asymptotic efficiency 🎬 13 min
5. Hypothesis Testing 7 lessons · 100 min
  1. 33 Hypotheses, errors and power 🎬 15 min
  2. 34 p-values and significance 🎬 15 min
  3. 35 The Neyman–Pearson lemma and likelihood ratio tests 🎬 14 min
  4. 36 t-tests 🎬 13 min
  5. 37 Chi-squared tests 🎬 13 min
  6. 38 F-tests and ANOVA 🎬 14 min
  7. 39 Nonparametric tests 🎬 16 min
6. Regression and Linear Models 5 lessons · 82 min
  1. 40 Simple linear regression 🎬 15 min
  2. 41 Multiple regression in matrix form 🎬 16 min
  3. 42 Model diagnostics 🎬 17 min
  4. 43 Generalized linear models 🎬 16 min
  5. 44 Ridge and lasso regularization 🎬 18 min
7. Bayesian Statistics 5 lessons · 78 min
  1. 45 Prior and posterior distributions 🎬 15 min
  2. 46 Conjugate priors 🎬 16 min
  3. 47 Credible intervals 🎬 15 min
  4. 48 Bayesian vs. frequentist 🎬 17 min
  5. 49 Bayes factors 🎬 15 min
8. Stochastic Processes 5 lessons · 76 min
  1. 50 Markov chains 🎬 15 min
  2. 51 Poisson processes 🎬 15 min
  3. 52 Random walks 🎬 15 min
  4. 53 Brownian motion 🎬 15 min
  5. 54 Martingales 🎬 16 min
9. Measure-Theoretic Probability (optional) 5 lessons · 79 min
  1. 55 Sigma-algebras and measurable spaces 🎬 16 min
  2. 56 Probability measures 🎬 15 min
  3. 57 Lebesgue integration and expectation 🎬 15 min
  4. 58 Convergence theorems 🎬 16 min
  5. 59 Radon–Nikodym and conditional expectation 🎬 17 min
10. Information Theory 4 lessons · 59 min
  1. 60 Entropy 🎬 14 min
  2. 61 Cross entropy 🎬 16 min
  3. 62 KL divergence 🎬 14 min
  4. 63 Mutual information 🎬 15 min
11. Monte Carlo Methods 4 lessons · 58 min
  1. 64 Sampling 🎬 14 min
  2. 65 Rejection sampling 🎬 14 min
  3. 66 Monte Carlo integration 🎬 15 min
  4. 67 Importance sampling 🎬 15 min

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