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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)
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)
We show in this paper that the AGM postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of obserwtions. We remedy this weakness by augmenting the AGM system with four additional postulates, which are sound relative to a qualitative version of probabilistic(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)
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)
Recent progress towards unifying the probabilistic and preferential models semantics for nonmonotonic reasoning has led to a remarkable observation: Any consistent system of default rules imposes an unambiguous and natural ordering on these rules which, to emphasize its simple and basic character, we term "Z-ordering." This ordering can be used with various(More)