Unit notes

The units below are the teaching spine of the course:

• Week 0 — Readiness and the probability bridge
• Week 1 — Statistical experiments, models, parameters, and estimands
• Week 2 — Joint, conditional, and transformed distributions
• Week 3 — Random samples, order statistics, and exponential-family structure
• Week 4 — Exact sampling distributions, pivots, and normal theory
• Week 5 — Convergence, the laws of large numbers, and the delta method
• Week 6 — Estimation: moments, bias, variance, and consistency
• Week 7 — Likelihood, score, Fisher information, and maximum likelihood
• Week 8 — Synthesis and likelihood computation
• Week 9 — Bayesian estimation: prior, posterior, prediction, and loss
• Week 10 — Sufficiency, factorization, and data reduction
• Week 11 — Rao-Blackwell improvement, completeness, and UMVU estimation
• Week 12 — Information bounds, efficiency, and asymptotic normality
• Week 13 — Interval estimation and the shape of uncertainty
• Week 14 — Robustness, misspecification, and identification boundaries
• Week 15 — Synthesis and the bridge to Mathematical Statistics II