Subset simulation for problems with strongly non-Gaussian, highly anisotropic, and degenerate distributions

Abstract

Results from subset simulation often have significant variability that can be attributed to sample fluctuation and correlation among the conditional samples. In extreme cases, such as when conditional distributions are highly anisotropic or degenerate, sample correlation can cause conditional sampling to break down, resulting in failed subset simulations. To address the extreme cases where subset simulation breaks down, we propose to use an affine invariant ensemble MCMC sampler for conditional sampling. Unlike traditional MCMC algorithms used in subset simulation that use a single proposal density per subset or adapts the proposal in a heuristic manner, the proposed scheme automatically varies the step size with each move. The algorithm is particularly effective for estimating failure probabilities when the conditional probability density is strongly non-Gaussian and degenerates to possess a lower effective dimension. Two added benefits are that it allows subset simulation to be performed directly with non-Gaussian, highly dependent, or implicitly defined random variables and the method has only a single parameter. Therefore it is not sensitive to the many parameters that must be calibrated for the proposal density in conventional algorithms. Several examples are considered, each illustrating the benefit of the proposed methodology for different classes of problems.