Schedule

Term Fall 2026: 2026-08-24 through 2026-12-15.

Unit	Topic focus
Week 0 — Readiness and the probability bridge	joint marginal and conditional distributions, transformations and Jacobians, expectation covariance and generating functions, common families, laws of large numbers and the central limit theorem, proof conventions and notation
Week 1 — Statistical experiments, models, parameters, and estimands	the observed-data model, parameter versus estimand, assumptions made explicit, scientific targets and identification, building a model ledger
Week 2 — Joint, conditional, and transformed distributions	joint and conditional densities, change of variables and Jacobians, distributions of functions of random variables, verifying a transformation by simulation
Week 3 — Random samples, order statistics, and exponential-family structure	the random-sample model, order statistics and their densities, exponential families and natural parameters, recurring likelihood and conjugacy patterns
Week 4 — Exact sampling distributions, pivots, and normal theory	the sampling distribution of a statistic, chi-square t and F, independence of the sample mean and variance, pivots and coverage as a repeated-sampling property
Week 5 — Convergence, the laws of large numbers, and the delta method	convergence in probability and in distribution, the weak law, the central limit theorem, Slutsky’s theorem, the delta method, approximation error across sample size and skewness
Week 6 — Estimation: moments, bias, variance, and consistency	the method of moments, bias and variance, mean squared error, consistency, comparing candidate estimators by simulation
Week 7 — Likelihood, score, Fisher information, and maximum likelihood	the likelihood function, the score and its properties, observed and expected Fisher information, maximum likelihood estimation, numerical optimization and likelihood surfaces, boundary and non-identifiability cases
Week 8 — Synthesis and likelihood computation	choosing a tool for a problem, integrating model derivation and estimation, reproducing and repairing a generated likelihood argument, what the first half established
Week 9 — Bayesian estimation: prior, posterior, prediction, and loss	prior and posterior distributions, conjugate families, posterior predictive distributions, loss and risk, frequentist operating characteristics of Bayes estimators
Week 10 — Sufficiency, factorization, and data reduction	sufficient statistics, the factorization theorem, minimal sufficiency, exponential families revisited, sufficiency versus scientific adequacy
Week 11 — Rao-Blackwell improvement, completeness, and UMVU estimation	conditioning on a sufficient statistic, the Rao-Blackwell theorem, completeness, the Lehmann-Scheffe theorem, verifying risk improvement by simulation
Week 12 — Information bounds, efficiency, and asymptotic normality	the Cramer-Rao information bound, regularity conditions, efficiency and relative efficiency, asymptotic normality of maximum likelihood estimators, exact variance versus asymptotic approximation
Week 13 — Interval estimation and the shape of uncertainty	pivotal intervals, likelihood-based intervals, posterior intervals, the bootstrap in preview, coverage compared with posterior probability, approximation failure under misspecification
Week 14 — Robustness, misspecification, and identification boundaries	what an estimator targets when the model is wrong, contamination and influence, randomization as an identification device, the same observed distribution under different causal stories
Week 15 — Synthesis and the bridge to Mathematical Statistics II	the course as one argument, an integrated estimator study, what testing and decision theory will add, resampling and robust inference in preview

The LMS remains authoritative for section logistics and graded details.