AI 中文总结
本研究探讨空间暴露场干预政策的因果识别条件，证明高斯变换下仅Cameron-Martin空间平移满足正性，并分析正性失效对加权与结构估计的影响，提出结构识别准则及权重发散结果。
AI 中文摘要
许多干预措施作用于整个空间暴露场。我们研究了这些干预措施所诱导的分布何时满足政策正性（policy positivity），以及其失效对通过加权和结构建模进行因果评估的影响。我们证明，对于变换后为高斯场的暴露场，满足正性的唯一可容许平移位于观测暴露场的Cameron-Martin空间上。在细尺度变化和正则性假设下，这些是该尺度上唯一可容许的逐点非递减政策。因此，常见规则（如在高斯尺度上的上限约束和比例削减）可能违反正性。Cameron-Martin范数同时控制权重变异性以及候选结果模型之间的分歧放大为政策估计之间的分歧。在没有正性的情况下，有界连续响应模型可以做出任意相似的观测预测，而其政策估计仍然分离。我们还给出了一个针对特定政策的准则，用于在给定实现暴露状态条件下进行结构识别。最后，当违反正性的政策在每一个有限表示中都允许权重存在时，其权重二阶矩在恢复完整场的嵌套细化下发散。这些结果促使我们在合理的结构模型范围内以及有限表示的细化下，评估指定政策效应的识别性和敏感性。
英文摘要
Many interventions act on an entire spatial exposure field. We study when their induced laws satisfy policy positivity and what its failure implies for causal evaluation through weighting and structural modelling. We show that, for post-transformation fields that are Gaussian, the only admissible translation that satisfy positivity lie on the Cameron-Martin space of the observed exposure field. Under fine-scale variation and regularity assumptions, these are the only admissible non-decreasing pointwise policies on that scale. Common rules, including binding caps and proportional reductions on the Gaussian scale can therefore violate positivity. The Cameron-Martin norm controls both weight variability and the amplification of disagreement between candidate outcome models into disagreement between policy estimates. Without positivity, bounded continuous response models can make arbitrarily similar observational predictions while their policy estimates remain separated. We also give a policy-specific criterion for structural identification conditional on a realised exposure state. Finally, when a policy violating positivity admits weights in every finite representation, their second moments diverge under nested refinement that recovers the full field. These results motivate assessing identification and sensitivity for the specified policy effect across plausible structural models and under refinement of finite representations.
