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.

翻译：识别原因的影响及原因的结果在几乎所有科学领域中都至关重要。然而，通常所需概率可能无法从现有数据源中完全识别。本文展示了在多种因果概率中仍可实现部分可识别性。我们将此称为“ε-可识别性”，并论证其在特定子群体行为可被限制在狭窄范围内时的有效性。特别地，我们展示了当允许此类约束时，原本不可识别的因果效应和反事实概率如何被严格限定。通常这些约束易于测量且可合理假设。最后，我们将ε-可识别性应用于单元选择问题。