An Idiosyncratic Sample of Applied Statistics

• Mathematical Foundations

• Inequalities and Identities

• Linear Algebra Primer

• Probability Foundations

• Sets, Combinatorics, and Probability

• Theories of Probability

• Probability, Random Vectors, and the Multivariate Normal Distribution

• Hypothesis tests, stratified tests

• Combining tests

• E-values

• Confidence sets

• Inference when there are nuisance parameters

• Causal inference

• Fisher’s exact test

• Models, response schedules, and estimators

• Pseudo-random numbers, integers, samples, and permutations

• Introduction to election auditing and the Kaplan-Markov Inequality

• Confidence bounds for the mean of finite populations

  • The Normal approximation and bootstrap percentile intervals

  • Duality between testing and confidence sets

  • Confidence sets derived from the Binomial

  • Lower confidence bounds for the mean via Markov’s Inequality and methods based on the Empirical Distribution

  • Confidence bounds via the Chebychev and Hoeffding Inequalities

  • Wald’s Sequential Probability Ratio Test (SPRT)

  • The SPRT for sampling without replacement

  • The SPRT with nuisance parameters

  • The Kaplan-Wald confidence bound

  • Dollar-Unit Sampling and taint

  • Penny sampling

  • Method shootout

• Tests based on martingales and supermartingales

• Introduction to permutation tests; application to gender bias in teaching evaluations

• Classical permutation tests based on ranks

• Tests of randomness and independence

• Simulating randomization for permutation tests

• Simulated \(P\)-values are exact \(P\)-values for randomized tests

• Abstract permutation tests using projections

• Statistical inference

• Bayesian and Frequentist Estimation and Inference

• Resampling methods

• Goodness of Fit Tests

• Models of Pandemics

• Election Audits

• The Child Online Protection Act and Internet Content Filtering: nonparametric confidence intervals for porn

• Where’s the beef? Transmissible Spongiform Encephalopathy and U.S. imports of Canadian cattle

• The EM algorithm (incomplete)

• P-values, Probability, Priors, Rabbits, Quantifauxcation, and Cargo-Cult Statistics