Foundations of Statistical Inference
Foundations of Statistical Inference
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Probability & Uncertainty
Foundations
Variance, SD & Standard Error
The Sampling Distribution
The Central Limit Theorem
CLT Simulator
LLN vs CLT
Inference
p-values & Confidence Intervals
Test Statistics
The Bootstrap
Bag of Little Bootstraps
Power, Alpha, Beta & MDE
Monte Carlo Experiments
Multiple Testing
OLS & the Linear Model
Regression & the CEF
Gauss-Markov & Gaussian Assumptions
The Algebra Behind OLS
Residuals & Controls
R-squared & Pseudo R-squared
Frisch-Waugh-Lovell
Omitted Variable Bias
Estimation
Method of Moments
Maximum Likelihood
Limited Dependent Variables
Generalized Method of Moments
Bayesian Estimation
Inference Diagnostics
Heteroskedasticity
Clustered SEs
The Delta Method
Measurement Error
Model Building
Bias-Variance Tradeoff
Model Selection
When Inference Breaks Down
Causal Thinking
From Correlation to Causation
Bayesian Thinking
Bayesian Updating
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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