🤖 AI Summary
This study addresses the challenge of estimating time-varying outage risk and quantifying uncertainty in restoration processes using county-level power outage data. The authors propose a hierarchical Bayesian model that employs cubic B-spline basis functions to capture smooth, nonlinear restoration trajectories and adopts a Beta-Binomial likelihood to account for overdispersion in customer counts. Information sharing across geographic groups is achieved through shared hyperpriors. This approach provides, for the first time in outage restoration analysis, well-calibrated uncertainty quantification, enabling robust inference even under data sparsity. Experiments on diverse outage events in southern Wisconsin demonstrate that the model’s posterior mean reproduces trapezoidal AUC point estimates while yielding reliable uncertainty intervals—unattainable with deterministic methods—thereby offering actionable insights for emergency planning and decision-making.
📝 Abstract
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.