  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.
