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 authors outline a cognitive and computational account of causal learning in children. They propose that children use specialized cognitive systems that allow them to recover an accurate "causal map" of the world: an abstract, coherent, learned representation of the causal relations among events. This kind of knowledge can be perspicuously understood in terms of the formalism of directed graphical causal models, or Bayes nets. Children's causal learning and inference may involve computations similar to those for learning causal Bayes nets and for predicting with them. Experimental results suggest that 2-to 4-year-old children construct new causal maps and that their learning is consistent with the Bayes net formalism.The input that reaches children from the world is concrete, particular, and limited. Yet, adults have abstract, coherent, and largely veridical representations of the world. The great epistemological question of cognitive development is how human beings get from one place to the other: How do children learn so much about the world so quickly and effortlessly? In the past 30 years, cognitive developmentalists have demonstrated that there are systematic changes in children's knowledge of the world. However, psychologists know much less about the representations that underlie that knowledge and the learning mechanisms that underlie changes in that knowledge.In this article, we outline one type of representation and several related types of learning mechanisms that may play a particularly important role in cognitive development. The representations are of the causal structure of the world, and the learning mechanisms involve a particularly powerful type of causal inference. Causal knowledge is important for several reasons. Knowing about causal structure permits us to make wide-ranging predictions about future events. Even more important, knowing about causal structure allows us to intervene in the world to bring about new eventsoften events that are far removed from the interventions themselves.

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.

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.

Three studies investigated whether young children make accurate causal inferences on the basis of patterns of variation and covariation. Children were presented with a new causal relation by means of a machine called the "blicket detector." Some objects, but not others, made the machine light up and play music. In the first 2 experiments, children were told that "blickets make the machine go" and were then asked to identify which objects were "blickets." Two-, 3-, and 4-year-old children were shown various patterns of variation and covariation between two different objects and the activation of the machine. All 3 age groups took this information into account in their causal judgments about which objects were blickets. In a 3rd experiment, 3- and 4-year-old children used the information when they were asked to make the machine stop. These results are related to Bayes-net causal graphical models of causal learning.

A fundamental task in various disciplines of science, including biology, is to find underlying causal relations and make use of them. Causal relations can be seen if interventions are properly applied; however, in many cases they are difficult or even impossible to conduct. It is then necessary to discover causal relations by analyzing statistical properties of purely observational data, which is known as causal discovery or causal structure search. This paper aims to give a introduction to and a brief review of the computational methods for causal discovery that were developed in the past three decades, including constraint-based and score-based methods and those based on functional causal models, supplemented by some illustrations and applications.

Problems involving causal inference have dogged at the heels of Statistics since its earliest days. Correlation does not imply causation and yet causal conclusions drawn from a carefully designed experiment are often valid. What can a statistical model say about causation? This question is addressed by using a particular model for causal inference (Rubin, 1974; Holland and Rubin, 1983) to critique the discussions of other writers on causation and causal inference. These include selected philosophers, medical researchers, statisticians, econometricians, and proponents of causal modelling.