Stat 992 - Research in Causal Inference (Spring 2025)

Tue. 1:00p.m. - 2:15p.m. at 6102 Social Sciences

• Course Overview
• Assignments, Quizzes, and Exams
• Lecture Notes

Instructor: Hyunseung Kang
Email: hyunseungWHALE@statWHALE.wisc.edu (remove all marine mammals from the e-mail address)
Office: 1245B Medical Sciences Center (MSC)
Syllabus: Syllabus

Course Overview

The purpose of the course is to prepare graduate students to start research in causal inference. At the end of the course, students will

1. Understand key concepts in causal inference (counterfactuals/potential outcomes, confounding, missing data)
2. Learn how to identify causal estimands
3. Learn how to estimate/infer causal estimands

Prerequisites

The official prerequisite for the course is to be in graduate/professional standing. The effective prerequisites are:

1. Working understanding of graduate-level probability theory, mathematical statistics, and linear models (i.e. at the level of Stat 609/610 and Stat 849/850). Specifically, you need to know
   • conditional expectations and independence
   • convergence of random variables
   • properties of maximum likelihood estimators
   • statistical properties of generalized linear models
   • Wald tests and likelihood ratio tests
   • nonparametric two-sample tests (e.g., permutation test)
2. Be able to design simulations that numerically validate properties of estimators (e.g. bias, variance, convergence) and statistical tests (e.g. Type I error rate, power, coverage of confidence intervals)
3. Working understanding of the software R (e.g. write/debug/test R code or install/run/work with existing R packages)

Assignment, Quizzes, and Exams

There are no exam and quizzes for grading.

There is one graded assignment, which is to summarize a paper listed in the syllabus; see the syllabus for more details. The assignment is due March 7, 2025, at 5:00pm Madison local time .

Lecture Notes

Every year, I focus on a couple of lecture notes to update based on (a) feedback from past students and (b) typos or mistakes. Also, while I'll try my best to correct typos or mistakes in the notes before lecture, feel free to ask me during lecture if you have any questions.

• Prerequisites: [slides], [html].
• Foundational concepts in causal inference: [slides], [html].
• Causation versus association
• Counterfactuals/potential outcomes
• Fundamental problem of causal inference
• Randomized experiments, connection to missing data, and covariate balance: [slides], [html].
• Identification under strong ignorability (i.e., no unmeasured confounding) and properties of the propensity score: [slides],[html].
• Identification of linear contrasts (CATE, ATE, ATT)
• Identification of non-linear contrasts (odds ratio, relative risk)
• Identification of policy functions (single-time optimal treatment regime OTR)
• Identification under unmeasured confounding (instrumental variables): [slides] [html].
• Identification under monotonicity (i.e., LATE; complier average treatment effect)
• Identification under no additive interaction assumption
• Estimation of causal parameters (Z estimators): [pdf].
  • There is a typo in Section 3.2 about the estimating equation for IPW estimator with estimated nuisance functions. The typo will corrected next year and I want to thanks Dr. Jieru Shi (University of Cambridge) for catching this.
• Estimation of causal parameters (Influence functions and von Mises expansion) [pdf].
• Identification under unmeasured confounding (regression discontinuity designs, differences-in-differences): Next year.
• Sensitivity analysis (Rosenbaum's model): [html].
• Summary of papers: [slides].