The goal of causal inference is the discovery of cause effect relationships from observational data, using appropriate assumptions. Two innovations that proved key for this task are a formal representation of potential outcomes under a random treatment assignment (due to Neyman), and viewing cause effect relationships via directed acyclic graphs (due to Wright). Using a modern synthesis of these two ideas, I consider the problem of mediation analysis which decomposes an overall causal effect into component effects corresponding to particular causal pathways. Simple mediation problems involving direct and indirect effects and linear models were considered by Baron and Kenny in the 1980s, and a significant literature has been developed since.

In this talk, I consider mediation analysis at its most general: I allow arbitrary models, the presence of hidden variables, multiple outcomes, longitudinal treatments, and effects along arbitrary sets of causal pathways. There are three distinct but related problems to solve – a representation problem (what sort of potential outcome does an effect along a set of paths correspond to), an identification problem (can a causal parameter of interest be expressed as a functional of observed data), and an estimation problem (what are good ways of estimating the resulting statistical parameter). I report a complete solution to the first two problems, and progress on the third. In particular, I show that for some parameters that arise in mediation settings a triply robust estimator exists, which relies on an outcome model, a mediator model, and a treatment model, and which remains consistent if any two of these three models are correct.

Some of the reported results are a joint work with Eric Tchetgen Tchetgen, Caleb Miles, Phyllis Kanki, and Seema Meloni.

## Speaker Biography

Ilya Shpitser is a Lecturer in Statistics at the University of Southampton. Previously, he was a Research Associate at the Harvard School of Public Health, working in the causal inference group with James M. Robins, Tyler VanderWeele, and Eric Tchetgen Tchetgen. His dissertation work was done at UCLA under the supervision of Judea Pearl. The fundamental question driving his research is this: “what makes it possible (or impossible) to infer cause-effect relationships?” Ilya received Ph.D. in Computer Science from UCLA in 2008. He then did a postdoctoral fellowship in the causal inference group at the Harvard School of Public Health until 2012.