6 articles.
The textbook confidence interval for a proportion has exact coverage you can compute by summing over the n+1 possible samples, and at n = 30 with p = 0.10 it is 0.8085 rather than 0.95. Coverage does not improve monotonically with n, and in a rare-event setting it can fall to 0.0392. Two one-line alternatives fix it.
On the burglary network with both neighbours calling, rejection sampling keeps 183 of 100,000 draws and likelihood weighting keeps all of them at an effective sample size of 396. Both estimates are about 10% off a posterior of 0.284172, and the reason is exactly computable: 252 samples carry 76% of the weight and 99.975% of the squared weight.
Estimators as random variables with distributions of their own, the case where the unbiased estimator is the worse one, what a confidence interval actually promises and the standard interval that delivers 87% where it advertises 95%, and what a p-value is a probability of - every figure computed exactly or by fixed-seed simulation.
Reasoning about what must be true: models and entailment worked by exhaustive enumeration, soundness and completeness, why propositional logic runs out of expressive power, and where first-order logic picks up.
Derive Bayes' theorem from the definition of conditional probability, then work the base-rate example that fools almost everyone, twice: once with the formula and once by pure counting.
The setup behind every predictive model: estimating an unknown function f from data, the split between reducible and irreducible error, and why prediction and inference pull in different directions.