Rare Event Estimation for Computer Models

Abstract

Rare events for computer models are usually impossible to address via direct methods—the conceptually straightforward approach of making millions of “ordinary” code runs to generate an adequate number of rare events simply is not an option. In Bayesian applications, the common practice of sampling from posterior distributions is inefficient for rare event estimation when some parameters are important, and corresponding normalized estimates can be seriously biased for seemingly adequate sample sizes (e.g., N = 10⁶). Rare event estimation based on adaptive importance sampling can improve computational efficiencies by orders of magnitude relative to ordinary simulation methods, greatly reducing the need for time-consuming code runs.

Keywords:

• Computer experiments
• Gaussian process
• Importance sampling
• Percentile estimation
• Quantile estimation
• Sequential experimental design