MCMC algorithms for Subset Simulation

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Estimation of the lower and upper bounds on the probability of failure using subset simulation and random set theory (2018, methodology): “In those cases, sensitivity analysis methods can also be used to address the situation (see e.g. Alvarez (2009b); Patelli et al. (2014)).”
Bayesian Updating with Structural Reliability Methods (2015, background): “…𝐮𝑖 (𝑗) , 𝑗 = 1, … , 𝐽 , from the (𝑛 + 1) -variate independent standard normal distribution conditional on Ω𝑖−1 , 𝜑𝑛+1(𝐮|Ω𝑖−1) , using a MCMC algorithm, e.g. (Au and Beck 2001) or (Papaioannou et al. 2014). c. Define the domain Ω𝑖 = {𝐻(𝐮) ≤ 𝑏𝑖}, wherein 𝑏𝑖 is chosen as the…”
Sequential importance sampling for structural reliability analysis (2016, methodology): “(26) has been used for sampling Gaussian process prior models [29] and has also been proposed for use within SuS [28].”
Rare event estimation with sequential directional importance sampling (2022, methodology): “2 Conditional sampling M-H (CSM-H) algorithm The second proposal distribution we used in this paper is the normal distribution conditioned on the current state (conditional M-H algorithm) [42, 43], i.”