Sequential Computer Experimental Design for Estimating an Extreme Probability or Quantile
This work addresses the challenge of efficient extreme event estimation in computational experiments, particularly for systems with random inputs, and is incremental in refining sequential design methods for practical application.
The paper tackles the problem of estimating extreme probabilities or quantiles from computer simulations without requiring large Monte Carlo experiments, by building a statistical surrogate and using sequential design to add runs, achieving improved estimates with modest computational effort.
A computer code can simulate a system's propagation of variation from random inputs to output measures of quality. Our aim here is to estimate a critical output tail probability or quantile without a large Monte Carlo experiment. Instead, we build a statistical surrogate for the input-output relationship with a modest number of evaluations and then sequentially add further runs, guided by a criterion to improve the estimate. We compare two criteria in the literature. Moreover, we investigate two practical questions: how to design the initial code runs and how to model the input distribution. Hence, we close the gap between the theory of sequential design and its application.