Foundations of Statistical Inference
Foundations of Statistical Inference
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Probability & Sampling
Summation Algebra
Foundations
Expected Value E(X)
Law of Iterated Expectations
Variance, SD & Standard Error
The Sampling Distribution
Law of Large Numbers
Central Limit Theorem
LLN vs CLT
Inference
From Normal to t
p-values & Confidence Intervals
Test Statistics
The Bootstrap
Bag of Little Bootstraps
Power, Alpha, Beta & MDE
Precise Null vs. Underpowered
Monte Carlo Experiments
Multiple Testing
Regression
Regression & the CEF
Deriving OLS (by hand)
The Algebra Behind OLS
Gauss-Markov & Gaussian Assumptions
Zero Conditional Mean
Sampling Distribution of OLS
Residuals & Controls
R-squared & Pseudo R-squared
Frisch-Waugh-Lovell
Omitted Variable Bias
From Correlation to Causation
Estimation
Method of Moments
Maximum Likelihood
Limited Dependent Variables
Generalized Method of Moments
Bayesian Estimation
Bayesian Updating
Bayesian Inference as Statistical Mechanics
Inference Diagnostics
Heteroskedasticity
Clustered SEs
The Delta Method
Measurement Error
Model Building
Bias-Variance Tradeoff
Model Selection
When Inference Breaks Down
Statistical Foundations of AI
Training as Maximum Likelihood
Regularization as Bayesian Inference
Prediction vs Causation in Foundation Models
Experimental Design for AI Systems
Calibration & Uncertainty Quantification
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