Multilevel Estimation of Rare Events

摘要: This work is motivated by the need to estimate probability of rare events in engineering systems with random inputs. We introduce a multilevel estimator which based on and generalizes idea subset simulation. The novel employs hierarchy approximations system response computed different resolutions. leads reduced computational costs compared study statistical properties implementation details proposed estimator. Markov chain Monte Carlo (MCMC) runs are required within estimator, we demonstrate that nestedness associated failure domains enables perfect MCMC simulation without burn-in. show follows from certain simple one-dimensional domains. In high dimensions propose modification uses level-dependent stochastic input dimensions. report numerical experiments one- two-dimensional physical space; particular, we...