One lecture session per week. Problem sets are due one week after the sessions they cover; see Assignments and Exams.
| Ses # | Topic | Deliverable |
|---|
| Part I · Probability and asymptotics |
| 1 | Probability Models, Random Variables, and Expectation | Probability derivations |
| 2 | Probability Distributions and Multivariate Models | Distribution and Jacobian exercises |
| 3 | Sampling Distributions and Asymptotic Theory | LLN/CLT and delta-method problems |
| Part II · Estimation and inference |
| 4 | Point Estimation: Moments, Likelihood, and Optimality | MLE derivation |
| 5 | Confidence Intervals and Hypothesis Testing | Testing report |
| 6 | Bayesian Inference, Conjugacy, and Posterior Computation | Conjugate posterior exercise |
| Part III · Experimental design and ANOVA |
| 7 | Experimental Design, Randomization, and Blocking | Randomization and blocking plan |
| 8 | ANOVA, Linear Contrasts, and Multiple Comparisons | Factorial analysis |
| Part IV · Statistical modeling |
| 9 | Linear Regression and Generalized Linear Models | Logistic/count model lab |
| 10 | Nonparametric Inference, Rank Tests, and Resampling | Rank/permutation analysis |
| 11 | Statistical Power, Sample Size, and Equivalence | Preregistered power plan |
| 12 | Linear Mixed Models and Hierarchical Data | Hierarchical model analysis |
| 13 | Multivariate Analysis: PCA, Covariance, and Dimension Reduction | PCA report |
| Part V · Statistical workflow |
| 14 | Statistical Modeling Workflow, Simulation, and Reproducibility | Statistical research project |