Thomas S. Richardson is a British-American statistician at the University of Washington whose work on graphical models and causal inference has provided essential theoretical tools for reasoning about causation when not all relevant variables are observed. His development of ancestral graphs, with Peter Spirtes and others, extended the graphical models framework to handle latent (hidden) variables and selection bias, situations that are ubiquitous in observational studies. His contributions have deepened the mathematical foundations of causal inference and expanded the range of problems where graphical methods can be reliably applied.
Life and Career
Born in the United Kingdom. Studies mathematics and statistics before moving to the United States for graduate work.
Earns his Ph.D. from Carnegie Mellon University under the supervision of Peter Spirtes and Thomas Dean, with a thesis on graphical models with latent variables.
Publishes foundational work on ancestral graphs with Peter Spirtes, providing a complete graphical framework for representing conditional independence under marginalization and conditioning.
Develops the single world intervention graph (SWIG) framework with James Robins, unifying graphical causal models with potential outcomes.
Continues to develop theoretical foundations for causal inference, including work on nested Markov models and identification in complex causal structures.
Ancestral Graphs
In many real-world problems, the causal graph includes variables that are unobserved or that are selected on (e.g., hospital patients who were selected for a study based on their symptoms). Standard directed acyclic graphs (DAGs) cannot directly represent the statistical implications of marginalizing over hidden variables or conditioning on selection variables. Richardson and Spirtes developed maximal ancestral graphs (MAGs) to fill this gap.
A MAG uses two types of edges: directed arrows (representing direct causal effects) and bidirected edges (representing the presence of latent common causes). The Markov properties of MAGs characterize exactly the conditional independence relations that hold in the observed data when some variables are hidden or selected on. This provides researchers with a graphical tool for reasoning about confounding and selection bias without requiring that all variables be measured.
In most observational studies, researchers cannot measure all potential confounders. Standard DAG-based methods require the full causal graph, including all latent variables, which is rarely available. Ancestral graphs work directly with the observed variables, encoding the constraints that latent common causes impose on the observed distribution. This makes them a practical tool for real-world causal reasoning, where the assumption that all relevant variables are observed is almost never satisfied.
Single World Intervention Graphs
One of Richardson's most important conceptual contributions, developed with James Robins, is the Single World Intervention Graph (SWIG) framework. SWIGs bridge the gap between Pearl's graphical causal models and Rubin's potential outcomes framework by representing potential outcomes as nodes in an augmented graph. This allows researchers to read off identification results for causal effects using graphical criteria while maintaining the precise counterfactual semantics of the potential outcomes framework.
The SWIG framework resolves longstanding tensions between the two dominant approaches to causal inference, showing that they are not merely equivalent in principle but can be combined in a single graphical representation that preserves the strengths of both.
Contributions to Graphical Model Theory
Beyond causal inference, Richardson has made fundamental contributions to the theory of graphical models, including work on the Markov properties of chain graphs, the equivalence classes of graphical models, and the algebraic structure of models with hidden variables. His work on nested Markov models characterizes the constraints that a DAG with hidden variables implies on the observed distribution, going beyond conditional independence to include equality constraints that provide additional testable implications.
"The power of graphical models lies in their ability to make complex assumptions transparent. When assumptions are transparent, they can be questioned, tested, and improved." — Thomas Richardson
Legacy
Richardson's work has provided the mathematical infrastructure that makes rigorous causal inference possible in realistic settings. By extending graphical methods to handle the latent variables and selection effects that pervade real-world data, he has expanded the applicability of causal reasoning from idealized settings to the messy reality of observational science. His bridging of the graphical and potential outcomes traditions through SWIGs represents a major intellectual achievement in the foundations of causal inference.