Subset Simulation is an adaptive simulation method that efficiently solves structural
reliability problems with many random variables. The method requires sampling from …

This accessible new edition explores the major topics in Monte Carlo simulation that have
arisen over the past 30 years and presents a sound foundation for problem solving …

Over forty years ago average-case error was proposed in the applied mathematics literature
as an alternative criterion with which to assess numerical methods. In contrast to worst-case …

This paper discusses a novel strategy for simulating rare events and an associated Monte
Carlo estimation of tail probabilities. Our method uses a system of interacting particles and …

The estimation of rare event or failure probabilities in high dimensions is of interest in many
areas of science and technology. We consider problems where the rare event is expressed …

Let X be a random vector with distribution μ on ℝ d and Φ be a mapping from ℝ d to ℝ. That
mapping acts as a black box, eg, the result from some computer experiments for which no …

Abstract Crude Monte-Carlo or quasi Monte-Carlo methods are well suited to characterize
events of which associated probabilities are not too low with respect to the simulation …

Many system reliability problems involve performance functions with a discontinuous
distribution. Such situations occur in both connectivity-and flow-based network reliability …

The use of proxy models for optimisation of expensive functions has demonstrated its value
since the 1990's in many industries. Within reservoir engineering, similar techniques have …

We present a versatile Monte Carlo method for estimating multidimensional integrals, with
applications to rare-event probability estimation. The method fuses two distinct and popular …