用于估计停电时变风险的分层样条贝塔-二项回归模型
Hierarchical Spline-Based Bayesian Beta-Binomial Regression for Estimating Time-Varying Risk in Power Outages
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中文总结 AI 辅助
该研究提出分层样条贝塔-二项回归模型，结合B样条与贝塔-二项似然，经PyMC的NUTS采样器推断，可估计停电时变风险，其AUC后验均值能提供校准不确定性，为公用事业及应急规划人员提供工具。
中文摘要 AI 辅助
我们提出了一种分层贝叶斯模型，用于从县级停电数据中估计时变停电风险。该模型将三次B样条基函数与贝塔-二项似然相结合，以捕捉平滑、非线性的恢复轨迹，同时适应观测到的用户数量的过度离散性。贝塔-二项集中参数的共享超先验支持地理索引组之间的分层收缩，允许稀疏或短暂事件从更广泛的总体中借用统计强度。后验推断通过PyMC中的无-U-Turn采样器（NUTS）进行，得到潜在停电概率和衍生恢复力指标（包括风险曲线下面积（AUC））的完整后验分布。我们使用后验预测覆盖率、RMSE和留一交叉验证评估预测性能，并在来自EAGLE-I停电监测平台的威斯康星州南部一组异质停电事件中验证了该模型。与朴素梯形AUC估计的直接比较证实，后验均值恢复了与确定性积分相同的点估计，同时提供了确定性方法在结构上无法实现的校准不确定性量化。该框架为公用事业和应急规划人员提供了一种原则性工具，用于在不确定性下对恢复动态进行基准测试和比较停电事件。
英文摘要
We propose a hierarchical Bayesian model for estimating time-varying outage risk from county-level power outage data. The model combines cubic B-spline basis functions with a Beta-Binomial likelihood to capture smooth, nonlinear recovery trajectories while accommodating overdispersion in observed customer counts. A shared hyperprior on the Beta-Binomial concentration parameter enables hierarchical shrinkage across geographically indexed groups, allowing sparse or short-lived events to borrow statistical strength from the broader population. Posterior inference is conducted via the No-U-Turn Sampler (NUTS) in PyMC, yielding full posterior distributions over latent outage probabilities and derived resilience metrics including the area under the risk curve (AUC). We assess predictive performance using posterior predictive coverage, RMSE, and leave-one-out cross-validation, and demonstrate the model across a heterogeneous set of outage events in southern Wisconsin drawn from the EAGLE-I power outage monitoring platform. A direct comparison against naive trapezoidal AUC estimation confirms that the posterior mean recovers the same point estimates as deterministic integration while providing calibrated uncertainty quantification that deterministic approaches structurally cannot. The framework offers utilities and emergency planners a principled tool for benchmarking recovery dynamics and comparing outage events under uncertainty.
