Importance Sampling

Focusing on fast stochastic simulation, this research monograph highlights the significance of importance sampling (IS) for estimating probabilities of rare events in scientific and engineering contexts. It emphasizes an adaptive IS approach that enhances simulation efficiency, crucial for understanding rare occurrences that can lead to severe consequences, such as structural failures or environmental disasters. The text traces the historical development of Monte Carlo methods and their broad applications in complex engineering problems where analytical solutions are challenging.