A separated splitting technique for disconnected rare event sets

Abstract

A key challenge for an efficient splitting technique is defining the importance function. If the rare event set consists of multiple separated subsets this challenge becomes bigger since the most likely path to the rare event set may be very different from the most likely path to an intermediate level. We propose to mitigate this problem of path deviation by estimating the subset probabilities separately using a modified splitting technique. We compare the proposed separated splitting technique with a standard splitting technique by estimating the probability of entering either of two separated intervals on the real line. The squared relative error of the estimator is shown to be significantly higher when using standard splitting than when using separated splitting. We show that this difference increases if the rare event probability becomes smaller, illustrating the advantage of the separated splitting technique.

Rare event simulation for steady-state probabilities via recurrency cycles

“…. , m following the loglinear interpolation approach from Wadman et al (2014). Assuming (I-II) are satisfied, the MLS method with these parameters should give the desired relative error, as in (5.5).…”

A Large-Deviation-Based Splitting Estimation of Power Flow Reliability

“…Details behind splitting can be found in for example [Garvels, 2000, Rubino and Tuffin, 2009, L'Ecuyer et al, 2006, Botev and Kroese, 2012. To keep this paper self-contained we give a brief introduction, similar to that in [Wadman et al, 2014]. Any splitting technique starts by defining an importance function h : [0, T ]× R n → R that assigns a value to each chain state (t, x).…”

“…In a simple case with a one-dimensional state space and an interval as the rare event set, the distance to the rare event set will serve as a suitable importance function [L'Ecuyer et al, 2006, Wadman et al, 2014. In many other cases however, the choice for the importance function is more difficult.…”