单调响应处理的有价值效应概率
Probability of worthwhile effect of monotone-response treatments
AI总结：
研究在处理效应非负（单调处理响应）情况下，通过显式构造依赖方案，解决处理效应超过给定值的最佳和最坏情况概率问题，该问题在不同背景下有等效描述。
AI中文摘要：
实验设计可能使我们无法在单个受试者身上观察到对一种处理及其缺失的响应。因此，两种情况的边际分布可能可观测，但联合分布不可观测，从而模糊了处理效应的分布。我们研究了处理效应非负（即单调处理响应）的情况，这在许多实际应用中是常见假设。我们通过为每种情况的依赖方案进行显式构造，解决了处理效应超过给定值的最佳和最坏情况概率问题。这些问题在不同背景下可等效描述为依赖不确定性和序约束下的风险聚合，以及具有特定成本函数的最优运输问题。
英文摘要：
Experiments may, by design, prevent one from observing on a single subject both the response to a treatment and to its absence. Because of this, marginal distributions for both cases may be observable but not their joint distribution, thus obscuring the distribution of the treatment effect. We examine the case where we impose that the treatment effect is nonnegative, also called monotone treatment response, a common assumption relevant to many practical applications. We solve the problems of best- and worst-case probabilities that the treatment effect exceeds a given value, using an explicit construction for the dependence scheme in each case. Such problems can equivalently be described, in different contexts, as risk aggregation under dependence uncertainty and an order constraint, and as optimal transport with a particular cost function.
