AI 中文总结
该研究针对多元宇宙分析，提出分布几何框架，以概率分布表示规范，定义分布距离，通过局部邻域等研究多元宇宙，数值示例和实际案例表明此方法能补充现有总结，保留效应与不确定性变化。
AI 中文摘要
多元宇宙分析明确了实证结论如何依赖于替代的、合理的分析规范。标准方法通常先生成多元宇宙，然后通过决策表、规范曲线、模型权重或标量输出（如估计值和p值）进行总结。这种分阶段的观点很有用，但它可能会掩盖推理不确定性在不同规范中的分布情况。我们提出了一个分布几何框架，其中每个可接受的规范由公共目标输出空间上的概率分布表示。在定义了这些分布之间的合适距离后，诱导的几何结构允许通过局部邻域、直径、弗雷歇重心和离散度测量来研究多元宇宙分析。数值示例和实际案例研究说明了该方法如何通过保留效应变化和不确定性变化来补充现有的多元宇宙总结。
英文摘要
Multiverse analysis makes explicit how empirical conclusions depend on alternative, defensible analytical specifications. Standard approaches usually generate the multiverse first and then summarize it through decision tables, specification curves, model weights, or scalar outputs such as estimates and \textit{p}-values. This stagewise view is useful, but it can hide how inferential uncertainty is arranged across specifications. We propose a distributional-geometric framework in which each admissible specification is represented by a probability distribution on a common target-output space. After defining a suitable distance between these distributions, the induced geometry allows the multiverse of analyses to be studied through local neighbourhoods, diameters, Fréchet barycentres, and dispersion measures. Numerical examples alongside a real case study illustrate how the approach complements existing multiverse summaries by retaining both effect variation and uncertainty variation.
Comments21 pages, 6 figures
