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Suppose you survey students in your class and discover that a higher proportion of students who smoke received a final grade of A than do students who do not smoke. Possible data are displayed in Table 1: 50 percent of the 10 smokers received an A, and only 40 percent of the five nonsmokers received an A. Puzzled by the seeming implication that smoking(More)
Causal diagrams have a long history of informal use and, more recently, have undergone formal development for applications in expert systems and robotics. We provide an introduction to these developments and their use in epidemiologic research. Causal diagrams can provide a starting point for identifying variables that must be measured and controlled to(More)
The direct effect of one event on another can be defined and measured by holding constant all intermediate variables between the two. Indirect effects present conceptual and prac­ tical difficulties (in nonlinear models), be­ cause they cannot be isolated by holding cer­ tain variables constant. This paper presents a new way of defining the effect transmit­(More)
The primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject-matter information. In particular, the paper develops a principled, nonparametric framework for causal inference, in which diagrams are queried to determine if the assumptions available are sufficient for identifying(More)
This review presents empirical researcherswith recent advances in causal inference, and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those(More)
Belief networks are directed acyclic graphs in which the nodes represent propositions (or variables), the arcs signify direct dependencies between the linked propositions, and the strengths of these dependencies are quantified by conditional probabilities. A network of this sort can be used to represent the generic knowledge of a domain expert, and it turns(More)