I enjoy working on causal inference in randomized experiments.

We think in terms of what would happen (**potential outcomes**),
and what could have happened (**counterfactuals**).

Loh, W. W., & Richardson, T. S. (2015).
A Finite Population Likelihood Ratio Test of the Sharp Null Hypothesis for Compliers.
*In Thirty-First Conference on Uncertainty in Artificial Intelligence.*

Paper

R package

Loh, W. W., & Richardson, T. S. (2013).
A Finite Population Test of the Sharp Null for Compliers.
*In UAI Workshop on Approaches to Causal Structure Learning, 15 July, Bellevue, Washington.*

Paper

The idea of simulating potential outcomes is nicely described in this episode of the TV show **Person of Interest**:
If-Then-Else.