Schedule

A schedule of topics and readings is provided below. Each week covers a single topic or group of topics. You should make sure to review the readings prior to that week’s lectures with an aim towards completing them before Wednesday’s lecture.

Textbook readings are from Aronow and Miller, Foundations of Agnostic Statistics, which is available through the UW-Madison library. All hyperlinks to papers and to other books are either to the published version or to a freely available copy.

This course begins on Tuesday, September 8. Wednesday, September 2nd is cancelled due to the American Political Science Association (APSA) annual meeting.

Week 1: Introduction and Foundations of Probability

Tuesday, September 8 & Wednesday, September 9

Topics:

  • Course introduction: what is statistics for, and what is this sequence for?
  • Sample spaces, events, and the probability measure
  • The axioms of probability and their implications

Readings:

  • Section 1.1; Aronow, Peter M., and Benjamin T. Miller. 2019. Foundations of Agnostic Statistics. Cambridge: Cambridge University Press.
  • Software familiarization: Chapters 1-4 and 28 (“Quarto”); Wickham, Hadley, Mine Çetinkaya-Rundel, and Garrett Grolemund. 2023. R for Data Science, 2nd ed.

Problem Set 1 assigned Tuesday, September 8 – due Tuesday, September 22.

Week 2: Conditional Probability and Independence

Tuesday, September 15 & Wednesday, September 16

Topics:

  • Conditional probability and the law of total probability
  • Independence and conditional independence
  • Reasoning with Bayes’ rule

Readings:

Week 3: Random Variables, Expectations

Tuesday, September 22 & Wednesday, September 23

Topics:

  • Random variables as functions on the sample space
  • Defining a distribution: CDFs, PMFs and PDFs
  • Properties of random variables: expected value and variance

Readings:

Problem Set 1 due Tuesday, September 22. Problem Set 2 assigned Tuesday, September 22 – due Tuesday, October 6

Week 4: Joint and Conditional Distributions

Tuesday, September 29 & Wednesday, September 30

Topics:

  • Joint, marginal and conditional distributions
  • Conditional expectation functions and the “best linear predictor”
  • Covariance and correlation
  • Law of iterated expectations

Readings:

Week 5: Estimands as features of distributions

Tuesday, October 6 & Wednesday, October 7

Topics:

  • Defining estimands as statistical functionals
  • Connecting theory to empirical targets

Readings:

Problem Set 2 due Tuesday, October 6. Problem Set 3 assigned Tuesday, October 6 – due Tuesday, October 20

First Midterm Exam - Wednesday, October 7th

Week 6: Estimation: Part 1

Tuesday, October 13 & Wednesday, October 14

Topics:

  • Random sampling from a target population
  • Properties of estimators: bias, variance and consistency
  • Convergence in probability and the weak law of large numbers

Readings:

Week 7: Estimation: Part 2

Tuesday, October 20 & Wednesday, October 21

Topics:

  • Convergence in distribution and the central limit theorem
  • Plug-in estimators of statistical functionals
  • Density estimation

Readings:

Problem Set 3 due Tuesday, October 20. Problem Set 4 assigned Tuesday, October 20 – due Tuesday, November 3

Replication project memo due Wednesday, October 21

Week 8: Confidence Intervals and Hypothesis Testing

Tuesday, October 27 & Wednesday, October 28

Topics:

  • Standard errors and the construction of confidence intervals
  • Hypothesis tests, test statistics and p-values
  • The bootstrap

Readings:

Week 9: Introduction to Regression

Tuesday, November 3 & Wednesday, November 4

Topics:

  • Ordinary least squares as an estimator of the Best Linear Predictor
  • Classical OLS and estimation of the conditional expectation function
  • Properties of the OLS estimator

Readings:

Problem Set 4 due Tuesday, November 3. Problem Set 5 assigned Tuesday, November 3 – due Tuesday, November 17

Week 10: Inference for Regression

Tuesday, November 10 & Wednesday, November 11

Topics:

  • Sampling distribution of the OLS estimator
  • Heteroskedasticity-consistent standard errors
  • Classical OLS standard errors under homoskedasticity

Readings:

Week 11: Interpreting Regressions

Tuesday, November 17 & Wednesday, November 18

Topics:

  • Interpreting multiple regression and the Frisch-Waugh-Lovell theorem
  • Interactions, summarizing partial derivatives and “marginal effects”

Readings:

Problem Set 5 due Tuesday, November 17.

Second Midterm Exam - Wednesday, November 18

Week 12: Regression wrap-up

Tuesday, November 24

Topics:

  • Polynomial regression, sieve estimators
  • Overfitting and penalized regression

Thanksgiving recess runs November 26-29. Class meets as usual on Tuesday this week.

Week 13: Weighting estimators

Tuesday, December 1 & Wednesday, December 2

Topics:

  • Missing data, bounds for the sample mean, and assumptions for point identification
  • Horvitz-Thompson and Hájek inverse probability weighting estimators
  • Post-stratification/raking weights in surveys.

Readings:

Fall Grad Poster Presentations at MEAD, Friday 12/4, 1:30-4pm Ogg Room

Week 14: Preview: Causal inference

Tuesday, December 8 & Wednesday, December 9

Topics:

  • The potential outcomes model for causal inference
  • The fundamental problem of causal inference
  • The “credibility revolution” and the centrality of research design

Readings: