Bounding rare event probabilities in computer experiments

We are interested in bounding probabilities of rare events in the context of computer experiments. These rare events depend on the output of a physical model with random input variables. Since the model is only known through an expensive black box function, standard efficient Monte Carlo methods designed for rare events cannot be used. We then propose a strategy to deal with this difficulty based on importance sampling methods. This proposal relies on Kriging metamodeling and is able to achieve sharp upper confidence bounds on the rare event probabilities. The variability due to the Kriging metamodeling step is properly taken into account. The proposed methodology is applied to a toy example and compared to more standard Bayesian bounds. Finally, a challenging real case study is analyzed. It consists of finding an upper bound of the probability that the trajectory of an airborne load will collide with the aircraft that has released it.Comment: 21 pages, 6 figure

Computer‐simulated experiments and computer games: A method of design analysis

This paper describes a new research programme to design computer‐simulated experiments in the field of fuels and combustion, and describes a method of categorization based on a taxonomy proposed by Gredler. The key features which enhance science content and process skills are identified The simulations are designed to be as realistic as possible, and are built using three‐dimensional computer‐aided design, rendering and animation tools, with the intention of creating an interactive virtual laboratory on the computer screen. A number of computer games are also categorized against the computer simulations and the same taxonomy for comparison. The paper then describes how designers of computer simulations can add to their own learning by retrospectively analysing their own simulations