Department of Statistics, UCLA

This paper deals with the problem of esti- mating the probability that one event was the cause of another in a given scenario. Us- ing structural-semantical de nitions of the probabilities of necessary or su cient cau- sation (or both), we show how to optimally bound these quantities from data obtained in experimental and observational studies, given various assumptions concerning the data-generating process. In particular, we strengthen the results of Pearl (1999) by weakening the data-generation assumptions and deriving theoretically sharp bounds on the probabilities of causation. These results delineate precisely the assumptions that must be made before statistical measures (such as the excess-risk-ratio) could be used for as- sessing attributional quantities (such as the probability of causation).