A multilevel Monte Carlo method for computing failure probabilities
arXiv:1408.6856 · doi:10.1137/140984294
Abstract
We propose and analyze a method for computing failure probabilities of systems modeled as numerical deterministic models (e.g., PDEs) with uncertain input data. A failure occurs when a functional of the solution to the model is below (or above) some critical value. By combining recent results on quantile estimation and the multilevel Monte Carlo method we develop a method which reduces computational cost without loss of accuracy. We show how the computational cost of the method relates to error tolerance of the failure probability. For a wide and common class of problems, the computational cost is asymptotically proportional to solving a single accurate realization of the numerical model, i.e., independent of the number of samples. Significant reductions in computational cost are also observed in numerical experiments.
References in corpus (3)
Cited by in corpus (11)
- Estimation of distributions via multilevel Monte Carlo with stratified sampling
- Multifidelity probability estimation via fusion of estimators
- Multilevel Sequential Importance Sampling for Rare Event Estimation
- A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data
- On the Calibration of Multilevel Monte Carlo Ensemble Forecasts
- Modern Monte Carlo Methods for Efficient Uncertainty Quantification and Propagation: A Survey
- Analysis of nested multilevel Monte Carlo using approximate Normal random variables
- Multilevel Monte Carlo Simulations of Composite Structures with Uncertain Manufacturing Defects
- Improved Multilevel Monte Carlo Methods for Finite Volume Discretisations of Darcy Flow in Randomly Layered Media
- Quasi-Monte Carlo and Multilevel Monte Carlo Methods for Computing Posterior Expectations in Elliptic Inverse Problems
- Scheduling massively parallel multigrid for multilevel Monte Carlo methods