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.

中文翻译：

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具有强非高斯、高度各向异性和退化分布的问题的子集模拟

摘要 子集模拟的结果通常具有显着的可变性，这可以归因于条件样本之间的样本波动和相关性。在极端情况下，例如当条件分布高度各向异性或退化时，样本相关性会导致条件采样失效，从而导致子集模拟失败。为了解决子集模拟失败的极端情况，我们建议使用仿射不变集成 MCMC 采样器进行条件采样。与子集模拟中使用的传统 MCMC 算法对每个子集使用单个建议密度或以启发式方式调整建议不同，所提出的方案会自动改变每次移动的步长。当条件概率密度是强非高斯的并且退化为具有较低的有效维度时，该算法对于估计故障概率特别有效。两个额外的好处是它允许直接使用非高斯、高度相关或隐式定义的随机变量执行子集模拟，并且该方法只有一个参数。因此，它对传统算法中必须为建议密度校准的许多参数不敏感。考虑了几个例子，每个例子都说明了所提出的方法对不同类别问题的好处。或隐式定义的随机变量，并且该方法只有一个参数。因此，它对传统算法中必须为建议密度校准的许多参数不敏感。考虑了几个例子，每个例子都说明了所提出的方法对不同类别问题的好处。或隐式定义的随机变量，并且该方法只有一个参数。因此，它对传统算法中必须为建议密度校准的许多参数不敏感。考虑了几个例子，每个例子都说明了所提出的方法对不同类别问题的好处。