MCMC algorithms for Subset Simulation

• We review and assess MCMC algorithms for application within Subset Simulation.
• We propose a novel MCMC approach that performs conditional sampling in the standard normal space.
• We propose a variant of the new approach with adaptive scaling.
• We demonstrate that the proposed adaptive approach enhances the efficiency of Subset Simulation.

Subset Simulation is an adaptive simulation method that efficiently solves structural reliability problems with many random variables. The method requires sampling from conditional distributions, which is achieved through Markov Chain Monte Carlo (MCMC) algorithms. This paper discusses different MCMC algorithms proposed for Subset Simulation and introduces a novel approach for MCMC sampling in the standard normal space. Two variants of the algorithm are proposed: a basic variant, which is simpler than existing algorithms with equal accuracy and efficiency, and a more efficient variant with adaptive scaling. It is demonstrated that the proposed algorithm improves the accuracy of Subset Simulation, without the need for additional model evaluations.