  This paper deals with the problem of estimating the probability that one
event was a cause of another in a given scenario. Using structural-semantical
definitions of the probabilities of necessary or sufficient causation (or
both), we show how to optimally bound these quantities from data obtained in
experimental and observational studies, making minimal 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 how empirical data can be used both in settling questions of
attribution and in solving attribution-related problems of decision making.
