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
• Multiple testing
• E-values and betting scores
• 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
  • Tests based on betting martingales: choosing the bet
• 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