Quantitative assessment of extinction risk requires confidence intervals (CIs) that remain informative with limited data. Their usefulness has long been debated because short observation spans can make uncertainty so large that population viability analysis appears impractical. I derive new CIs for extinction probability under the drift-Wiener process, a canonical model of extinction dynamics, by introducing transformed parameters $w$ and $z$ whose maximum-likelihood estimators follow noncentral $t$ distributions. The resulting $w$-$z$ method yields CIs with coverage close to the nominal level and shows that precision depends not only on data length but also on effect size: extinction probabilities that are sufficiently low or high can often be estimated reliably even from limited time series. I also propose an observation-error-and-autocovariance-robust (OEAR) estimator for settings with additive observation error and short-run dependence. Applied to two 64-year national harvest indices for Japanese eel (Anguilla japonica), the method gives Criterion E extinction probabilities far below the IUCN threatened-category thresholds, with narrow CIs, despite the species being listed as Endangered under Criterion A. These results show that extinction-risk CIs can be both statistically rigorous and practically informative for conservation assessment under limited data.

翻译：定量评估灭绝风险需要能够在有限数据下保持信息量的置信区间（CIs）。由于观测时间跨度较短可能导致不确定性过大，使得种群生存力分析显得不切实际，其有用性长期存在争议。本文针对漂移-维纳过程（一种经典的灭绝动态模型），通过引入变换参数$w$和$z$（其最大似然估计量服从非中心$t$分布），推导出灭绝概率的新置信区间。由此建立的$w$-$z$方法产生的置信区间覆盖概率接近名义水平，并表明精度不仅取决于数据长度，还取决于效应大小：即使基于有限时间序列，足够低或足够高的灭绝概率通常也能被可靠估计。针对存在加性观测误差和短期依赖性的场景，本文进一步提出一种观测误差与自协方差稳健（OEAR）估计量。将该方法应用于日本鳗鲡（Anguilla japonica）的两个64年全国捕捞量指数，结果显示：尽管该物种根据标准A被列为濒危物种，但其标准E下的灭绝概率远低于IUCN受威胁类别阈值，且置信区间范围狭窄。这些结果表明，在数据有限的保护评估中，灭绝风险置信区间既能保持统计严谨性，又能提供具有实践意义的参考信息。