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
- Understand key concepts in causal inference (counterfactuals/potential outcomes, confounding, missing data)
- Learn how to identify causal estimands
- 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:
- 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)
- 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)
- 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
- 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 unmeasured confounding (regression discontinuity designs, differences-in-differences)
- Estimation of causal parameters (M/Z estimators) and double robustness: [pdf].
- Estimation of causal parameters (Influence functions, von Mises expansion, semiparametric efficiency) and cross-fitting (double machine learning) [pdf].
- Sensitivity analysis (Rosenbaum's model): [html].