Subset Simulation is a Markov chain Monte Carlo method that was initially conceived to compute small failure probabilities in structural reliability problems. This is done by iteratively sampling from nested subsets on the input space of a performance function. Subset Simulation has since been adapted to perform as a sampler in other realms such as optimisation, Bayesian updating and history matching. In all of these contexts, it can be that either the geometry of the input domain or the nature of the corresponding performance function cause Subset Simulation to suffer from ergodicity problems. This paper proposes an enhancement to Subset Simulation called Branching Subset Simulation. The proposed framework uses a nearest neighbours algorithm and Voronoi diagrams to partition 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.
翻译：子集模拟是一种 Markov 链 Monte Carlo 方法,最初设计该方法是为了计算结构可靠性问题中的小故障概率。这是通过在性能函数输入空间上从嵌套子子子组中迭代取样完成的。 子集模拟后来被调整为在优化化、 巴伊西亚更新和历史匹配等其他领域作为取样员发挥作用。 在所有这些情况下, 可能是输入域的几何或相应的性能函数的性质导致子集模拟遭受过敏问题。 本文建议对子集模拟进行升级, 称为分流子集模拟模拟。 拟议的框架使用近邻算法和沃罗诺伊图来分割输入空间, 并在每个分区中开始分流化子集模拟。 这表明, 分解子集模拟比子集模拟更不可能遭受过过过过过敏的问题, 并且提高了取样效率 。
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