Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in settings with discrete treatment and discrete ordinal outcome. We propose new families of monotonicity assumptions and formulate the bounding problem as a linear programming problem. We further introduce a new monotonicity assumption specifically to achieve identification. Finally, we present numerical experiments to validate our methods and demonstrate their application using real-world datasets.

翻译：评估潜在结果与观测变量的联合概率及其线性组合是因果推断中的基本挑战。本文探讨了在离散处理与离散有序结果设定下这些概率的界与识别问题。我们提出了新的单调性假设族，并将界估计问题构建为线性规划问题。进一步地，我们引入了一种专门用于实现识别的新单调性假设。最后，我们通过数值实验验证了所提方法，并利用真实数据集展示了其应用。