Spring 2026 · UPF Graphical models, causal discovery, latent variables, interference, and positive dependence.
This course studies modern structured statistical methods for applied economics, with a focus on graphical models, causal discovery, latent-variable models, interference, and positive dependence.
Piotr Zwiernik
Email: piotr.zwiernik@upf.edu
Office hours: 20.202 by appointment
This is not a causal inference course but this area of data analysis relies heavily on similar ideas. I will try to make my lecture as self-contained as possible but some material that may be useful:
| Lecture | Topic | Slides |
|---|---|---|
| 1 | Conditional independence as structure | Lecture1 |
| 2 | Gaussian and non-paranormal graphical models | Lecture2 |
| 3 | DAGs, Markov equivalence, and interventions | Lecture3 |
| 4 | Causal discovery, linear structural equation models, and non-Gaussian identification | Lecture4 |
| 5 | Latent variable models — from trees to neural nets | Lecture5 |
| 6 | Unobserved confounding and adjustments | Lecture6 |
| 7 | Positive dependence and total positivity | Lecture7 |
| 8 | Network interference and spillovers | Lecture8 |
| 9-10 | Presentations |
See the proposed project topics.