内生停止下二元实验的序关系
Ranking Experiments under Sequential Sampling
中文总结 AI 辅助
该研究针对内生停止下的二元统计实验，引入停止优势与决策优势两种序关系并证明其一致性，通过定向Kullback-Leibler散度刻画，还提出精确模拟定理以生成目标实验，为相关决策问题提供理论支撑。
中文摘要 AI 辅助
我们研究大样本下二元统计实验的比较，其中信息是序贯获取的，观测次数可依赖于已实现的证据。我们引入两种序关系：停止优势通过实验复现任意停止策略结果的能力来比较实验，决策优势则通过实验在观测成本高昂的有限决策问题中的价值来比较实验。我们的主要结果表明，这两种序关系是一致的，且由两个定向Kullback-Leibler散度的逐坐标优势所刻画。此外，严格优势意味着在任何学习状态可改变最优行动的决策问题中，最终会呈现严格的价值优势。该刻画背后的关键结果是一个精确模拟定理：任何二元目标实验都可通过对源实验的重复观测生成，其期望样本量可达到两个KL下界，仅相差一个仅依赖于源的加性常数。
英文摘要
We compare statistical experiments when observations are inexpensive and can be acquired sequentially until the decision maker chooses to stop. We introduce two orders. Small-cost decision dominance asks which of two equally priced experiments is eventually preferred in every decision problem as the per-observation cost vanishes; large-budget stopping dominance asks which experiment can reproduce every terminal experiment attainable from the other under all sufficiently large expected-sample budgets. Our main result shows that, for generic pairs, the two orders coincide and are both characterized by strict dominance of every pairwise Kullback--Leibler divergence. The key step is a uniform exact-conversion theorem: any finite-output stopping policy based on one experiment can be reproduced exactly using another, with first-order expected-sample requirements determined by pairwise KL rates and a square-root remainder that is uniform over policies.
