目标感知的序贯推断：合并与分层任意有效设计
Target-Aware Sequential Inference: Pooled versus Stratified Anytime-Valid Designs
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中文总结 AI 辅助
该研究针对异质分层序贯研究中的目标感知推断，比较合并与分层设计，推导最优分配指数和2/3规则，证明方差自适应的重要性，并展示合并推断可显著降低停止成本。
中文摘要 AI 辅助
具有异质分层的序贯研究通常以加权总体均值为目标，同时在一种不同的、可能自适应的分配下收集数据。这产生了两个不同的设计选择：观察值如何分配，以及推断是直接针对目标进行，还是通过聚合同时的分层置信序列进行。我们在任意有效推断下比较这些架构。对于单个预先指定的目标，直接目标抽样产生一个有界的合并过程。当需要同时进行分层报告、事后重新加权或对多个目标的稳健性时，分层构造会聚合局部置信序列。对于具有幂律速率n的负beta次方的局部半宽度，我们推导出渐近宽度最优分配；其指数为1/(1+beta)，并且根号n方差自适应边界产生2/3规则。我们在可预测的自适应抽样下建立有效性，在消失的探索下限下显示预言机跟踪，将设计扩展到不确定的目标分布和族级最优系统识别，并量化不必要的局部多重性的首阶成本。模拟和公共基准回放显示了两个稳健模式：方差自适应可能比精细分配调整更重要，并且当不需要局部同时保证时，合并的目标特定推断可以显著降低停止成本。该框架通过一个共同的目标感知序贯设计问题将分层抽样、置信序列、自适应分配以及排序和选择联系起来。
英文摘要
Sequential studies with heterogeneous strata may define the estimand under a target mixture that differs from the sampling distribution. We organize the design problem by guarantee class: one pooled confidence sequence for a single prespecified target, shared pooled inference for a prespecified target set, and stratum-resolved inference when local guarantees must remain available. For target-set pooled inference we derive minimax, gap-aware, and range-capped shared proposals and an adaptive tracking rule. A specialized augmented off-policy score removes between-stratum mean heterogeneity asymptotically, recovering Neyman allocation for efficient single-target pooled inference. Robust directional certification over a convex target set is a classical intersection-union problem and does not require an M-fold vertex split. We derive a Gaussian information lower bound and an exact finite-support characteristic information that coincides with the bounded nonparametric KL-inf limit, and state sufficient conditions for first-order attainment of the Gaussian constant. Within the local-CS architecture, regularly varying boundaries imply a general allocation law with the 2/3 exponent for root-n variance-adaptive widths. Simulations and a PromptEval replay illustrate the resulting guarantee-efficiency frontier.
发表机构
- Michigan State University（密歇根州立大学）
机构由 AI 辅助整理，请以论文原文为准。
