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Peter Spirtes develops mathematical and computational methods for causal discovery. His work asks which causal conclusions can be recovered from statistical data and background knowledge when fully controlled experiments are unavailable, and how to turn the corresponding guarantees into practical algorithms.^[ref]

With Clark Glymour and Richard Scheines, he coauthored Causation, Prediction, and Search by Peter Spirtes, Clark Glymour and Richard Scheines. One important example is the PC algorithm, which uses conditional independence information to remove candidate edges and orient some of the remaining ones. Under its assumptions, the resulting graph represents an equivalence class of possible causal explanations; it need not recover every arrow in a unique graph. Making these limitations explicit is part of the method's contribution, rather than an exception to it.^[ref]

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]