  Identifying the effects of causes and causes of effects is vital in virtually
every scientific field. Often, however, the needed probabilities may not be
fully identifiable from the data sources available. This paper shows how
partial identifiability is still possible for several probabilities of
causation. We term this epsilon-identifiability and demonstrate its usefulness
in cases where the behavior of certain subpopulations can be restricted to
within some narrow bounds. In particular, we show how unidentifiable causal
effects and counterfactual probabilities can be narrowly bounded when such
allowances are made. Often those allowances are easily measured and reasonably
assumed. Finally, epsilon-identifiability is applied to the unit selection
problem.
