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By Thomas S. Richardson, Robin J. Evans, James M. Robins, Ilya Shpitser.

Byline verified in the primary arXiv record. Introduction and section on latent projections: directed mixed graphs for margins of hidden-variable directed acyclic graphs.

Robin J. Evans studies causal inference, graphical models and the behavior of statistical models after hidden variables are marginalized. His work on margins of Bayesian networks characterizes algebraic restrictions that are not captured by a list of conditional independences alone.^[ref]

With Thomas S. Richardson and other collaborators, he coauthored Nested Markov Properties for Acyclic Directed Mixed Graphs by Thomas S. Richardson and others. A central idea is to describe constraints on the observed distribution without committing to an identifiable parameter for every unobserved mechanism.^[ref]

This matters when two models agree on ordinary independence tests yet differ in other restrictions on probabilities. Separating these cases can improve both model interpretation and estimation: a convenient parameterization of the observed model need not identify the underlying hidden causal story. His institutional personal-page redirect leads to his research-group site.^[ref]

Thomas S. Richardson develops graphical approaches to causal inference and statistical models, including ways to reason when some variables are hidden. His institutional research description lists graphical models, model selection, Bayesian inference and causal models.^[ref]

He is a coauthor of Nested Markov Properties for Acyclic Directed Mixed Graphs by Thomas S. Richardson and others. The work represents observable constraints of hidden-variable directed graphs using a nested Markov model. Its motivation is that eliminating a hidden cause can leave more than ordinary conditional independence restrictions among the measured variables.^[ref]

For example, a hidden common cause of two observed variables can be represented by a bidirected edge in a latent projection. The graph records a possible dependence source without pretending that the common cause itself was measured. Such representations separate what observations constrain from what remains unidentifiable.