While average treatment effects (ATE) and conditional average treatment effects (CATE) provide valuable population- and subgroup-level summaries, they fail to capture uncertainty at the individual level. For high-stakes decision-making, individual treatment effect (ITE) estimates must be accompanied by valid prediction intervals that reflect heterogeneity and unit-specific uncertainty. However, the fundamental unidentifiability of ITEs limits the ability to derive precise and reliable individual-level uncertainty estimates. To address this challenge, we investigate the role of a cross-world correlation parameter, $ ρ(x) = cor(Y(1), Y(0) | X = x) $, which describes the dependence between potential outcomes, given covariates, in the Neyman-Rubin super-population model with i.i.d. units. Although $ ρ$ is fundamentally unidentifiable, we argue that in most real-world applications, it is possible to impose reasonable and interpretable bounds informed by domain-expert knowledge. Given $ρ$, we design prediction intervals for ITE, achieving more stable and accurate coverage with substantially shorter widths; often less than 1/3 of those from competing methods. The resulting intervals satisfy coverage guarantees $P\big(Y(1) - Y(0) \in C_{ITE}(X)\big) \geq 1 - α$ and are asymptotically optimal under Gaussian assumptions. We provide strong theoretical and empirical arguments that cross-world assumptions can make individual uncertainty quantification both practically informative and statistically valid.

翻译：尽管平均处理效应（ATE）和条件平均处理效应（CATE）提供了有价值的群体和子群体层面的总结，但它们未能捕捉个体层面的不确定性。对于高风险决策，个体处理效应（ITE）估计必须伴随能够反映异质性和单元特定不确定性的有效预测区间。然而，ITE的固有不可识别性限制了推导精确且可靠的个体层面不确定性估计的能力。为应对这一挑战，我们研究了跨世界相关性参数 $ ρ(x) = cor(Y(1), Y(0) | X = x) $ 的作用，该参数在具有独立同分布单元的Neyman-Rubin超总体模型中描述了给定协变量时潜在结果之间的依赖关系。尽管 $ρ$ 本质上是不可识别的，但我们论证在大多数实际应用中，可以基于领域专家知识施加合理且可解释的边界。给定 $ρ$，我们设计了ITE的预测区间，实现了更稳定、更准确的覆盖率，且区间宽度大幅缩短——通常不到竞争方法的1/3。所得区间满足覆盖率保证 $P\big(Y(1) - Y(0) \in C_{ITE}(X)\big) \geq 1 - α$，并在高斯假设下渐近最优。我们通过坚实的理论与实证论证表明，跨世界假设能够使个体不确定性量化既具备实际信息价值，又具有统计有效性。