An improved likelihood-weighted sequential sampling method for extreme events statistics

In this work, we aim to improve the sequential sampling method which estimates the extreme-event statistics in response of a system subject to probabilistic input. The central part of sequential sampling is the acquisition based on which the next sample is selected. Among various kinds of acquisitions, the likelihood-weighted one (Blanchard & Spasis 2021) is among the most successful developments and has been applied to quantify extreme-event statistics in different contexts (e.g., extreme ship motion in waves, pandemic burst, along with other applications in Bayesian optimization, UAV path planning, and multi-arm bandit). This acquisition, however, assumes that the predicted output is sufficiently close to the ground truth. With only a limited number of samples available due to high evaluation costs, this condition can hardly be satisfied. Considering that, we improve the likelihood-weight acquisition by remedying the potential discrepancy between the prediction and ground truth. The new acquisition demonstrates significant improvements in a large number of synthetic cases with varying response functions (dimensions, variations, continuity) and a real-world application for quantifying extreme ship statistics.