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Richard Scheines studies causal discovery: learning causal structure from statistical evidence under explicit assumptions. With Peter Spirtes, Clark Glymour and collaborators, he developed the Tetrad research programme, connecting causal inference, algorithms and machine learning.^[ref]

In Causation, Prediction, and Search by Peter Spirtes, Clark Glymour and Richard Scheines, the collaborators examine how patterns of conditional independence constrain a causal directed acyclic graph. The connection is informative but conditional: faithfulness of a directed acyclic graph, restrictions on unobserved causes and the correctness of the independence information affect what can be identified. Different graphs can remain indistinguishable under Markov equivalence of directed acyclic graphs, so observational data need not select one unique causal story.^[ref]

Robert Tibshirani develops methods for statistical learning and biostatistics, with applications to genomics and medicine. His Stanford research profile connects methodological work with scientific data and computational tools.^[ref]

With Jerome H. Friedman and Trevor Hastie, he developed the Graphical Lasso for estimating a sparse precision matrix. An absolute-value penalty encourages zero entries, which encode conditional independence relationships in a multivariate normal distribution. The method combines a statistical model with an efficient optimization algorithm.^[ref]

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.

An unshielded collider in a directed acyclic graph is a triple $a\to b\leftarrow c$ with $a$ and $c$ nonadjacent. The absence of an edge between its outer vertices makes this orientation detectable from conditional independence information under faithfulness of a directed acyclic graph.

A Verma constraint is an equality restriction on an observed distribution implied by a latent-variable causal graph that need not be a conditional independence. Such constraints can therefore distinguish latent causal models whose ordinary observed conditional-independence relations coincide.