MULTILEVEL SEQUENTIAL IMPORTANCE SAMPLING FOR RARE EVENT ESTIMATION

The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit state function, which depends on the solution of a partial differential equation (PDE). Since numerical evaluations of PDEs are computationally expensive, estimating such probabilities of failure by Monte Carlo sampling is intractable. We develop a novel estimator based on a sequential importance sampler using discretizations of PDE-based limit state functions with different accuracies. A twofold adaptive algorithm ensures that we obtain an estimate based on the desired discretization accuracy. Moreover, we suggest and study the choice of the Markov chain Monte Carlo kernel for use with sequential importance sampling. Instead of the popular adaptive conditional sampling method, we propose a new algorithm that uses independent proposals from an adaptively constructed von Mises-Fisher-Nakagami distribution.