The correct inferential object in claims reserving is the conditional predictive distribution $p(R \mid \mathcal{D}, \hatθ)$, where $\mathcal{D}$ is the observed triangle held fixed. We refer to this as the conditioning principle. All existing bootstraps violate it by resampling functions of $\mathcal{D}$ inside the predictive loop, producing an $O(1)$ coverage error that does not vanish as the triangle grows. The Dirichlet-Gamma hierarchy admits a bootstrap that satisfies the principle exactly: $S^{IBNP}_i = X^{obs}_i (1-W_i)/W_i$ with $W_i \sim \mathrm{Beta}(c\hat{F}_{I-i}, c(1-\hat{F}_{I-i}))$ sampled directly from its predictive distribution. Only the allocation proportion $W_i$ is simulated; the observed triangle is held fixed. It thus inherits calibration from any development-proportion method (Chain-Ladder, Bornhuetter-Ferguson, Cape Cod, or other), making it model-agnostic. The coverage deficit is $O(I^{-1/2})$, independent of the number of development periods. Under compound Poisson data-generating processes the bootstrap is conservative for every $F_{I-i} \in (0,1)$: the predictive standard deviation analytically exceeds the true value by the factor $1/\sqrt{F_{I-i}}$. The ODP bootstrap violates the principle through two mechanisms in opposite directions: re-estimation inflates bootstrap variance under the ODP DGP, while missing accident-year frailty deflates it under frailty DGPs. The resulting coverage discrepancy is $Ω(1)$ regardless of $I$, providing a structural explanation for the cross-portfolio miscalibration heterogeneity documented by Meyers (2015). Chain-Ladder, Bornhuetter-Ferguson and Cape Cod emerge as credibility estimators under diffuse, informative and pooling priors respectively, with identical structure for counts and amounts. The concentration $c$ serves as a diagnostic: $\hat{c} < 30$ signals non-stationary development.

翻译：赔款准备金中正确的推断对象是条件化预测分布 $p(R \mid \mathcal{D}, \hatθ)$，其中 $\mathcal{D}$ 是固定不变的已观测三角形。我们将其称为条件化原则。所有现有的自助法均因在预测循环内对 $\mathcal{D}$ 的函数进行重采样而违反该原则，由此产生的 $O(1)$ 覆盖误差不会随三角形增大而消失。Dirichlet-Gamma层级结构提供了一种精确满足该原则的自助法：直接从其预测分布中抽取 $W_i \sim \mathrm{Beta}(c\hat{F}_{I-i}, c(1-\hat{F}_{I-i}))$，并通过公式 $S^{IBNP}_i = X^{obs}_i (1-W_i)/W_i$ 计算。仅分配比例 $W_i$ 被模拟，而观测三角形保持不变。因此，该方法继承自任何发展比例方法（链梯法、Bornhuetter-Ferguson法、Cape Cod法或其他方法）的校正特性，实现模型无关性。覆盖误差为 $O(I^{-1/2})$，与发展周期数无关。在复合泊松数据生成过程下，该自助法对于每一个 $F_{I-i} \in (0,1)$ 均具有保守性：预测标准差解析地超出真实值，倍数为 $1/\sqrt{F_{I-i}}$。ODP自助法通过两种方向相反的机制违反条件化原则：在ODP DGP下重估计膨胀了自助方差，而在非中心参数DGP下缺失的事故年脆弱性则紧缩了方差。由此产生的覆盖差异为 $Ω(1)$ 且与 $I$ 无关，这为Meyers（2015）所记录的跨组合校正异质性提供了结构性解释。链梯法、Bornhuetter-Ferguson法和Cape Cod法分别作为在扩散先验、信息先验和合并先验下的可信度估计量出现，且计数与金额具有相同结构。集中度参数 $c$ 可作为诊断指标：$\hat{c} < 30$ 指示非平稳发展。