Description
A mathematical and applied course in probability, statistical inference, Bayesian methods, experimental design, regression, generalized linear models, nonparametric methods, power, mixed models, and multivariate analysis.
Prerequisites
Calculus, linear algebra, and introductory statistics. Students should use R or Python for computational assignments.
Learning outcomes
Students will formulate probability models; derive estimators and sampling distributions; conduct likelihood and Bayesian inference; design experiments; analyze factorial and hierarchical data; fit GLMs; plan power; and produce reproducible statistical analyses.
14-week plan
| Week | Lecture | Deliverable |
|---|---|---|
| 1 | Probability models and expectation | Probability derivations |
| 2 | Distributions and multivariate models | Distribution and Jacobian exercises |
| 3 | Sampling and asymptotics | LLN/CLT and delta-method problems |
| 4 | Point estimation | MLE derivation |
| 5 | Confidence intervals and testing | Testing report |
| 6 | Bayesian inference | Conjugate posterior exercise |
| 7 | Experimental design | Randomization and blocking plan |
| 8 | ANOVA and multiple comparisons | Factorial analysis |
| 9 | Regression and GLMs | Logistic/count model lab |
| 10 | Nonparametric inference | Rank/permutation analysis |
| 11 | Power and sample size | Preregistered power plan |
| 12 | Mixed models | Hierarchical model analysis |
| 13 | Multivariate analysis | PCA report |
| 14 | Simulation and reproducibility | Statistical research project |
Assessment
| Component | Weight |
|---|---|
| Mathematical problem sets | 25% |
| Computational labs | 20% |
| Midterm | 20% |
| Experimental design / power report | 15% |
| Final reproducible project | 20% |
Core references
Casella and Berger, Statistical Inference; Lehmann and Romano, Testing Statistical Hypotheses; van der Vaart, Asymptotic Statistics; Gelman et al., Bayesian Data Analysis; Montgomery, Design and Analysis of Experiments; McCullagh and Nelder, Generalized Linear Models.