We introduce the Skipping Sampler, a novel algorithm to efficiently sample from the restriction of an arbitrary probability density to an arbitrary measurable set. Such conditional densities can arise in the study of risk and reliability and are often of complex nature, for example having multiple isolated modes and non-convex or disconnected support. The sampler can be seen as an instance of the Metropolis-Hastings algorithm with a particular proposal structure, and we establish sufficient conditions under which the Strong Law of Large Numbers and the Central Limit Theorem hold. We give theoretical and numerical evidence of improved performance relative to the Random Walk Metropolis algorithm.
The frequency stability of power systems is increasingly challenged by various types of disturbance. In particular, the increasing penetration of renewable energy sources is increasing the variability of power generation while reducing system inertia against disturbances. In this paper we explore how this could give rise to rate of change of frequency (RoCoF) violations. Correlated and non -Gaussian power disturbances, such as may arise from renewable generation, have been shown to be significant in power system security analysis. We therefore introduce ghost sampling which, given any unconditional distribution of disturbances, efficiently produces samples conditional on a violation occurring. Our goal is to address questions such as “which generator is most likely to be disconnected due to a RoCoF violation?” or “what is the probability of having simultaneous RoCoF violations, given that a violation occurs?”