Subset Simulation is a Markov chain Monte Carlo method, initially conceived to compute small failure probabilities in structural reliability problems. This is done by iteratively sampling from nested subsets in the input space of a performance function. Subset Simulation has since been adapted as a sampler in other realms such as optimisation, Bayesian updating and history matching. In all of these contexts, it is not uncommon that either the geometry of the input domain or the nature of the corresponding performance function cause Subset Simulation to suffer from ergodicity problems. To address these problems, this paper proposes Branching Subset Simulation. The proposed framework dynamically partitions the input space, and recursively begins Branching Subset Simulation anew in each partition. It is shown that Branching Subset Simulation is less likely than Subset Simulation to suffer from ergodicity problems and has improved sampling efficiency in the presence of multi-modality.

翻译：子集模拟是一种马尔可夫链蒙特卡洛方法，最初用于计算结构可靠性问题中的小失效概率。该方法通过迭代地从性能函数输入空间的嵌套子集中采样来实现。此后，子集模拟被改编为其他领域的采样工具，例如优化、贝叶斯更新和历史匹配。在这些应用中，输入域的几何形状或相应性能函数的性质常导致子集模拟出现遍历性问题。为应对这些问题，本文提出了分支子集模拟。所提出的框架动态划分输入空间，并在每个划分中递归地重新启动分支子集模拟。研究表明，分支子集模拟比标准子集模拟更不易出现遍历性问题，并且在存在多模态性的情况下具有更高的采样效率。