Much of epidemiology, econometrics, sociology and political science is an attempt to infer causal relationships using data gathered under conditions where fully controlled experiments are not possible. The goals of my current research (called the TETRAD project) can be divided into two main parts. The first goal is to specify and prove under what conditions it is possible to reliably infer causal relationships from background knowledge and statistical data not obtained under fully controlled conditions. The second goal is to develop, analyze, implement, test and apply practical, provably correct computer programs for inferring causal structure under conditions where this is possible. The results of this research are available in the TETRAD II computer program.

My research is interdisciplinary in nature, involving philosophy, statistics, graph theory and computer science. It has implications for the practices of a number of disciplines in which causal inferences from statistical data are made. The research that I have described shows that there are computer programs which can sometimes reliably draw useful causal conclusions under a reasonable set of assumptions. But there are still many cases where the assumptions I have made are known to be false. My current research centers on the extent to which these limiting assumptions can be relaxed, thereby extending the application of the results to a much wider class of phenomena, and investigating the extent to which these search procedures can be made more reliable on small samples. This research program has important theoretical and practical implications. Theoretically, it will help us understand the relationship between probability and causality, and what the precise limits of reliable inference from uncontrolled data are. Practically, it will provide a useful tool for scientists that will help them build causal models.

Spirtes, P., Zhang, J. (forthcoming) “A Uniformly Consistent Estimator of Causal Effects Under The k-Triangle-Faithfulness Assumption”, *Statistical Science*.

Spirtes, P., (2013) "Calculation of Entailed Rank Constraints in Partially Non-Linear and Cyclic Models", *Proceedings of the Twenty-Ninth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-13)*, AUAI Press, 2013, pp. 606-615.

Ramsey, J., Spirtes, P, and Glymour, C. (2011) “On meta-analyses of imaging data and the mixture of records.” *NeuroImage* **57**(2): 323-330.

Zhang, J., and Spirtes, P. (2011) "Intervention, Determinism, and the Causal Minimality Condition”, *Synthese*, 2011, **182:13**, pp. 335-347.

Ali, A., Richardson, T., Spirtes, P. (2009) “Markov Equivalence For Ancestral Graphs”, *Annals of Statistics*, **37**, 5B, 2808-2837.

Tillman, R., Gretton, A. and Spirtes, P. (2009) “Nonlinear directed acyclic structure learning with weakly additive noise models”, *NIPS 2009*.

Spirtes, P. (2009) "Variable Definition and Causal Inference", *Proceedings of the 13th International Congress of Logic Methodology and Philosophy of Science*, pp. 514-53.

Zhang, J., and Spirtes, P. (2009) "Detection of Unfaithfulness and Robust Causal Inference", *Minds and Machines*, 18:2, pp. 239-272.

Silva, R., Glymour, C., Scheines, R. and Spirtes, P. (2006) “Learning the Structure of Latent Linear Structure Models,” *Journal of Machine Learning Research*, 7, 191-246.

Ramsey, J., Zhang, J., and Spirtes, P., (2006) “Adjacency-Faithfulness and Conservative Causal Inference”, *Uncertainty in Artificial Intelligence 2006*, Boston, MA.

Spirtes, P. (2005) “Graphical Models, Causal Inference, and Econometric Models”, *Journal of Economic Methodology*. 2005 **12:1**, pp. 1–33.

Zhang, J., and Spirtes, P. (2005) “A Transformational Characterization of Markov Equivalence for Directed Acyclic Graphs with Latent Variables”, *Uncertainty in Artificial Intelligence 2005*, Edinboro, Scotland.

Ali, R., Richardson, T., Spirtes, P., and Zhang, J. (2005) “Towards Characterizing Markov Equivalence Classes for Directed Acyclic Graph Models with Latent Variables”, *Uncertainty in Artificial Intelligence 2005*, Edinboro, Scotland.

Spirtes, P., and Scheines, R. (2004). “Causal Inference of Ambiguous Manipulations”, in *Proceedings of the Philosophy of Science Association Meetings*, 2002.

Chu, T., Glymour, C., Scheines, R., Spirtes, P. (2003) “A Statistical Problem for Inference to Regulatory Structure from Associations of Gene Expression Measurements with Microarrays”, *Bioinformatics*, **19**, pp. 1147-1152.

Robins, J., Scheines, R., Spirtes, P., and Wasserman, L. (2003). “Uniform Consistency in Causal Inference”, *Biometrika*, September, **90**: pp. 491 – 515.

Zhang, J., and Spirtes, P. (2003) “Strong Faithfulness and Uniform Consistency in Causal Inference”, *UAI '03, Proceedings of the 19th Conference in Uncertainty in Artificial Intelligence*, August 7-10 2003, Acapulco, Mexico, ed. by Christopher Meek and Uffe Kjarulff, Morgan Kaufmann.

Richardson, T., Spirtes, P. (2002) “Ancestral Graph Markov Models”, *Annals of Statistics*, 2002, **30** pp. 962-1030.

Spirtes, P., Glymour, C. and Scheines, R. (2000). Causation, Prediction, and Search, 2nd ed. New York, N.Y.: MIT Press.

Spirtes, P., Glymour, C., and Scheines, R. (2000) Constructing Bayesian Network Models of Gene Expression Networks from Microarray Data, to appear in the Proceedings of the Atlantic Symposium on Computational Biology, Genome Information Systems & Technology.

Robins, J., Scheines, R., Spirtes, P., and Wasserman, L. (2000) Uniform Consistency in Causal Inference, Carnegie Mellon University Department of Statistics Technical Report 725.

Richardson, T., and Spirtes, P. (2000) Ancestral Markov Graphical Models, University of Washington Department of Statistics Technical Report 375.

Spirtes, P. (2000) An Anytime Algorithm for Causal Inference, to be presented at AI and Statistics 2001.

Spirtes, P. (1997). Limits on Causal Inference from Statistical Data, presented at American Economics Association Meeting.

Spirtes, P., Cooper, G. (1997). An Experiment in Causal Discovery Using a Pneumonia Database, Proceedings of AI and Statistics 99.

Spirtes, P., Richardson, T., Meek, C. (1997). The Dimensionality of Mixed Ancestral Graphs, Technical Report CMU-83-Phil.

Spirtes, P., Richardson, T., Meek, C., Scheines, R., and Glymour, C. (1997). Using Path Diagrams as a Structural Equation Modelling Tool, Technical Report CMU-82-Phil.

Scheines, R., Spirtes, P., Glymour, C., Meek, C., and Richardson, T. (forthcoming). The TETRAD Project: Constraint Based Aids to Causal Model Specification, Multivariate Behavioral Research

Spirtes, P., Glymour, C. and Scheines, R. (1993). Causation, Prediction, and Search, New York, N.Y.: Springer-Verlag.

Scheines, R. (forthcoming). An Introduction to Causal Inference, in Causality in Crisis, ed. by Steven Turner and Vaughan McKim, University of Notre Dame Press.

Spirtes, P., Richardson, T., Meek, C., Scheines, R., and Glymour, C., (1996). Using D-separation to Calculate Zero Partial Correlations in Linear Models with Correlated Errors, Technical Report CMU-72-Phil.

Spirtes, P., and Richardson, T. (1996). A Polynomial Time Algorithm For Determining DAG Equivalence in the Presence of Latent Variables and Selection Bias, Proceedings of the 6th International Workshop on Artificial Intelligence and Statistics.

Spirtes, P., Richardson, T., and Meek, C. (1996). Heuristic Greedy Search Algorithms for Latent Variable Models, Proceedings of the 6th International Workshop on Artificial Intelligence and Statistics.

Richardson, T., and Spirtes, P. (1996). Automated discovery of linear feedback models, Technical Report CMU-75-Phil.

Spirtes, P., and Scheines, R. (forthcoming). Reply to Freedman, in Causality in Crisis, ed. by Steven Turner and Vaughan McKim, University of Notre Dame Press.

Spirtes, P., Meek, C., and Richardson, T. (1996). Causal Inference in the Presence of Latent Variables and Selection Bias, Technical Report CMU-77-Phil.

Spirtes, P. (1995). Directed Cyclic Graphical Representation of Feedback Models, Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, ed. by Philippe Besnard and Steve Hanks, Morgan Kaufmann Publishers, Inc., San Mateo, 1995.

(P. Spirtes), "Calculation of Entailed Rank Constraints in Partially Non-Linear and Cyclic Models", Twenty-Ninth Conference Annual Conference on Uncertainty in Artificial Intelligence Press, August 11-15, 2013, Bellevue, WA.

(P. Spirtes) "Bayes Net Perspectives on Causation and Causal Inference", Causality: Perspectives from Different Disciplines, August 5-8, 2013, Vals, Switzerland.

(P. Spirtes), "Causal Search Algorithms, Graphical Models, and Experimentation", Causality and experimentation in the sciences", July 1-3, 2013, Paris, France.