A fundamental issue for theories of human induction is to specify constraints on potential inferences. For inferences based on shared category membership, an analogy, and/or a relational schema, it appears that the basic goal of induction is to make accurate and goal-relevant inferences that are sensitive to uncertainty. People can use source information at various levels of abstraction (including both specific instances and more general categories), coupled with prior causal knowledge, to build a causal model for a target situation, which in turn constrains inferences about the target. We propose a computational theory in the framework of Bayesian inference and test its predictions (parameter-free for the cases we consider) in a series of experiments in which people were asked to assess the probabilities of various causal predictions and attributions about a target on the basis of source knowledge about generative and preventive causes. The theory proved successful in accounting for systematic patterns of judgments about interrelated types of causal inferences, including evidence that analogical inferences are partially dissociable from overall mapping quality.