We obtained a new perspective on the enterprise from Judea Pearl's Probabilistic Reasoning in Intelligent Systems, which appeared the next year. Although not principally concerned with discovery, Pearl's book showed us how to connect conditional independence with causal structure quite generally, and that connection proved essential to establishing general, reliable discovery procedures. We have since profited from correspondence and conversation with Pearl and with Dan Geiger and Thomas Verma, and from several of their papers. Pearl's work drew on the papers of Wermuth (1980), Kiiveri and Speed (1982), Lauritzen (1983), andCarlin (1984), which in the early 1980s had already provided the foundations for a rigorous study of causal inference. Paul Holland introduced one of us to the Rubin framework some years ago, but we only recently realized it's logical connections with directed graphical models. We were further helped by J. Whittaker's (1990) excellent account of the properties of undirected graphical models.We have learned a great deal from Gregory Cooper at the University of Pittsburgh who provided us with data, comments, Bayesian algorithms and the picture and description of the ALARM network which we consider in several places. Over the years we have learned useful things from Kenneth Bollen. Chris Meek provided essential help in obtaining an important theorem that derives various claims made by Rubin, Pratt and Schlaifer from axioms on directed graphical models.Steve Fienberg and several students from Carnegie Mellon's department of statistics joined with us in a seminar on graphical models from which we learned a great deal. We are indebted to him for his openness, intelligence and helpfulness in our research, and to Elizabeth Slate for guiding us through several papers in the Rubin framework. We are obliged to Nancy Cartwright for her courteous but salient criticism of the approach taken in our previous book and continued here. Her comments prompted our work on parameters in Causation, Prediction, and Search Chapter 4. We are indebted to Brian Skyrms for his interest and encouragement over many years, and to Marek Druzdzel for helpful comments and encouragement. We have also been

To Martha, for her support and loveR .S. One source of the ideas in this book is in work we began ten years ago at the University of Pittsburgh. We drew many ideas about causality, statistics and search from the psychometric, economic and sociological literature, beginning with Charles Spearman's project at the turn of the century and including the work of Herbert Simon, Hubert Blalock and Herbert Costner. We obtained a new perspective on the enterprise from Judea Pearl's Probabilistic Reasoning in Intelligent Systems, which appeared the next year. Although not principally concerned with discovery, Pearl's book showed us how to connect conditional independence with causal structure quite generally, and that connection proved essential to establishing general, reliable discovery procedures. We have since profited from correspondence and conversation with Pearl and with Dan Geiger and Thomas Verma, and from several of their papers. Pearl's work drew on the papers of Wermuth (1980), Kiiveri and Speed (1982), Wermuth and Lauritzen (1983), and Kiiveri, Speed and Carlin (1984), which in the early 1980s had already provided the foundations for a rigorous study of causal inference. Paul Holland introduced one of us to the Rubin framework some years ago, but we only recently realized it's logical connections with directed graphical models. We were further helped by J. Whittaker's (1990) excellent account of the properties of undirected graphical models. We have learned a great deal from Gregory Cooper at the University of Pittsburgh who provided us with data, comments, Bayesian algorithms and the picture and description of the ALARM network which we consider in several places. Over the years we have learned useful things from Kenneth Bollen. Chris Meek provided essential help in obtaining an important theorem that derives various claims made by Rubin, Pratt and Schlaifer from axioms on directed graphical models. Steve Fienberg and several students from Carnegie Mellon's department of statistics joined with us in a seminar on graphical models from which we learned a great deal. We are indebted to him for his openness, intelligence and helpfulness in our research, and to Elizabeth Slate for guiding us through several papers in the Rubin framework. We are obliged to Nancy Cartwright for her courteous but salient criticism of the approach taken in our previous book and continued here. Her comments prompted our work on parameters in Causation, Prediction, and Search Chapter 4. We are indebted to Brian Skyrms for his interest and encouragement over many years, and to Marek Druzdzel for helpful comments and encouragement. We have also been

The heart of the scientific enterprise is a rational effort to understand the causes behind the phenomena we observe. In large-scale complex dynamical systems such as the Earth system, real experiments are rarely feasible. However, a rapidly increasing amount of observational and simulated data opens up the use of novel data-driven causal methods beyond the commonly adopted correlation techniques. Here, we give an overview of causal inference frameworks and identify promising generic application cases common in Earth system sciences and beyond. We discuss challenges and initiate the benchmark platform causeme.net to close the gap between method users and developers.

This paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all DAG independence models. This class of graphs, called maximal ancestral graphs, has two attractive features: there is at most one edge between each pair of vertices; every missing edge corresponds to an independence relation. These features lead to a simple parameterization of the corresponding set of distributions in the Gaussian case.

Previous asymptotically correct algorithms for recovering causal structure from sample probabilities have been limited even in sparse causal graphs to a few variables. We describe an asymptotically correct algorithm whose complexity for fixed graph connectivity increases polynomially in the number of vertices, and may in practice recover sparse graphs with several hundred variables. From sample data with n = 20,000, an implementation of the algorithm on a DECStation 3100 recovers the edges in a linear version of the ALARM network with 37 vertices and 46 edges. Fewer than 8% of the undirected edges are incorrectly identified in the output. Without prior ordering information, the program also determines the direction of edges for the ALARM graph with an error rate of 14%. Processing time is less than 10 seconds. Keywords DAGS, Causal Modelling.