# Sequential Computer Experimental Design for Estimating an Extreme Probability or Quantile

## TL;DR

This paper develops a sequential experimental design method to efficiently estimate extreme probabilities or quantiles of a system's output using a limited number of computer simulations, improving accuracy and practicality.

## Contribution

It introduces a sequential design approach for estimating tail probabilities with fewer simulations, comparing criteria and addressing initial design and input modeling.

## Key findings

- Effective sequential design criteria identified
- Method reduces number of simulations needed
- Guidelines for initial design and input modeling provided

## Abstract

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.