Fast Propagation of Epistemic Uncertainty in Seismic Hazard via Adaptive Importance Sampling

The conventional logic-tree approach used to represent epistemic uncertainty in probabilistic seismic hazard analysis (PSHA) is both computationally intensive and prone to introducing bias in hazard estimates. We propose a Gaussian Population Monte Carlo Adaptive Importance Sampling (G-PMC AIS) framework for PSHA computation to efficiently propagate epistemic uncertainty which uses the continuous distribution of uncertain model parameters. First, we demonstrate that the logic-tree approach introduces significant bias in mean and fractile hazards due to the ad hoc discretization and becomes computationally infeasible as the number of variables grows. We then present a mathematical formulation of PSHA using importance sampling (IS), illustrating how the IS optimal density enables efficient estimation of mean hazard and that its marginalization supports the fast computation of fractile hazards and sensitivity analysis. To efficiently approximate the optimal density and its marginalization, we adopt the G-PMC AIS framework within the IS formulation for PSHA. Numerical experiments show that our approach accelerates the computation of mean and fractile hazards and sensitivity metrics by factors of 13–224 compared to the logic-tree method, and 123–3,775 compared to Monte Carlo methods with continuous distributions. These gains are achieved while keeping the coefficient of variation (COV) of mean hazard below 1% and the Kolmogorov–Smirnov distance (K-S D) of fractile estimates from the true fractile below 5%. The proposed framework significantly reduces computational costs without compromising accuracy and is broadly applicable to PSHA projects.