← Back to Archive

Statistics

Course PDFs — full, modules, and lessons

Full course

Download full course PDF →

Module 1 — probability foundations

1.1 probability space 1.2 events sigma algebras 1.3 random variables 1.4 distribution functions 1.5 expectation 1.6 variance and covariance 1.7 conditional probability and expectation 1.8 law of large numbers 1.9 central limit theorem

Module 2 — statistical models

2.1 statistical models 2.2 sampling and data generating process 2.3 likelihood function 2.4 log likelihood and score 2.5 fisher information 2.6 exponential families

Module 3 — point estimation

3.1 estimators risk mse 3.2 method of moments and mle 3.3 properties of estimators 3.4 cramer rao lower bound 3.5 sufficiency rao blackwell lehmann scheffe 3.6 invariance and equivariance

Module 4 — interval estimation

4.1 confidence sets 4.2 pivotal quantities 4.3 likelihood based intervals 4.4 wald score lr intervals 4.5 asymptotic confidence theory 4.6 bootstrap confidence intervals

Module 5 — hypothesis testing

5.1 hypothesis testing framework 5.2 neyman pearson theory 5.3 uniformly most powerful tests 5.4 likelihood ratio tests 5.5 p values 5.6 duality tests confidence sets

Module 6 — bayesian inference

6.1 priors and posteriors 6.2 conjugate families 6.3 bayesian point estimation 6.4 credible sets 6.5 posterior predictive 6.6 bayes factors 6.7 bernstein von mises

Module 7 — asymptotic theory

7.1 modes of convergence 7.2 consistency 7.3 asymptotic normality 7.4 delta method 7.5 m estimation 7.6 likelihood asymptotics

Module 8 — multivariate linear models

8.1 random vectors and covariance 8.2 multivariate normal 8.3 linear models geometry ols 8.4 gauss markov theorem 8.5 inference in linear models 8.6 generalized linear models 8.7 principal component analysis

Module 9 — computational statistics

9.1 numerical optimization 9.2 monte carlo integration 9.3 markov chain monte carlo 9.4 bootstrap implementation 9.5 expectation maximization 9.6 variational inference

Module 10 — model selection learning

10.1 bias variance tradeoff 10.2 information criteria 10.3 cross validation 10.4 penalized likelihood regularization 10.5 high dimensional structure 10.6 model averaging

Module 11 — causality

11.1 potential outcomes 11.2 directed acyclic graphs 11.3 identifiability backdoor 11.4 randomized experiments 11.5 observational treatment estimation 11.6 policy evaluation structural