Complete written notes for each session. Every set of notes opens with learning objectives and closes with a problem set, a computational lab and readings. Use Print / save as PDF on any lecture page for an offline copy.
| Lec # | Topic and objectives | Length |
|---|---|---|
| Part I · Probability and asymptotics | ||
| 1 | Probability Models, Random Variables, and Expectation Define probability spaces and random variables; derive expectations and moments; work with conditional distributions; distinguish independence from zero correlation; apply iterated expectations and the law of total variance. | 9 min read |
| 2 | Probability Distributions and Multivariate Models Derive moments of standard distributions; transform random variables using Jacobians; obtain joint, marginal, and conditional distributions; interpret covariance matrices and multivariate normality. | 8 min read |
| 3 | Sampling Distributions and Asymptotic Theory Distinguish sampling distributions from population distributions; apply LLN, CLT, Slutsky, continuous mapping, and delta methods; understand bootstrap approximation. | 7 min read |
| Part II · Estimation and inference | ||
| 4 | Point Estimation: Moments, Likelihood, and Optimality Construct method-of-moments and maximum-likelihood estimators; derive score and information; distinguish unbiasedness, consistency, and efficiency; apply invariance and asymptotic theory. | 7 min read |
| 5 | Confidence Intervals and Hypothesis Testing Construct confidence intervals; formulate tests; derive size and power; interpret p-values; understand likelihood-ratio, Wald, and score tests; distinguish statistical and practical significance. | 8 min read |
| 6 | Bayesian Inference, Conjugacy, and Posterior Computation Derive posterior distributions; work with conjugate models; distinguish credible and confidence intervals; derive posterior predictions; assess prior sensitivity and MCMC computation. | 9 min read |
| Part III · Experimental design and ANOVA | ||
| 7 | Experimental Design, Randomization, and Blocking Define experimental units, treatments, outcomes, and estimands; explain randomization, blocking, replication, factorial and split-plot designs; connect assignment mechanisms to design-based inference. | 8 min read |
| 8 | ANOVA, Linear Contrasts, and Multiple Comparisons Derive one-way ANOVA; partition sums of squares; formulate contrasts; distinguish fixed and random effects; understand multiplicity adjustments and diagnostics. | 8 min read |
| Part IV · Statistical modeling | ||
| 9 | Linear Regression and Generalized Linear Models Derive the linear model; interpret conditional mean parameters; specify GLMs; interpret logistic and Poisson regression; assess overdispersion and diagnostics. | 8 min read |
| 10 | Nonparametric Inference, Rank Tests, and Resampling Use empirical distributions and quantiles; derive rank procedures; state the hypotheses actually tested; conduct permutation tests and bootstrap inference. | 7 min read |
| 11 | Statistical Power, Sample Size, and Equivalence Define power and minimum detectable effects; calculate sample sizes; account for clustering and attrition; distinguish non-significance from evidence of equivalence. | 8 min read |
| 12 | Linear Mixed Models and Hierarchical Data Specify random-intercept and random-slope models; distinguish within- and between-group effects; derive covariance structures and ICC; understand partial pooling and likelihood-based estimation. | 9 min read |
| 13 | Multivariate Analysis: PCA, Covariance, and Dimension Reduction Analyze covariance matrices; derive principal components; interpret eigenvalues and loadings; distinguish PCA from factor analysis; understand scaling and validation. | 8 min read |
| Part V · Statistical workflow | ||
| 14 | Statistical Modeling Workflow, Simulation, and Reproducibility Specify estimands and statistical models; design simulation studies; evaluate estimator performance; document computational decisions; report uncertainty and create reproducible archives. | 8 min read |