Introduction to Rare‐Event Simulation

Abstract

Without special techniques, simulation of rare events can be prohibitive due to the large amount of computer time needed. This article gives an introduction to methods that can be used to substantially reduce the variance associated with simulating rare events. Two broad classes of methods are discussed—importance sampling and splitting.

Efficient simulation of blackout probabilities using splitting

“…For a more extensive introduction, see Garvels [11], L'Ecuyer et al [16], Rubino and Tuffin [21], Shortle and L'Ecuyer [23]. The explanation given here is in the context of power-grid blackouts, though the discussion can be generalized to other applications.…”

A taxonomy of validation strategies to ensure the safe operation of highly automated vehicles

“…Another term often used in research regarding scenario-based validation is the term rare event. From the 47 papers considered in this review, 11 refer to rare events (Gietelink, 2007;Gietelink, De Schutter, & Verhaegen, 2005, 2006Hutchison et al, 2018;Koopman & Wagner, 2016;Shortle & L'Ecuyer, 2011;Zhao, 2016;Zhao, Huang, Peng, Lam, & LeBlanc, 2018;Zhao et al, 2017;Zlocki, Eckstein, & Fahrenkrog, 2015).…”

“…If the probability density function from where the random seeds are sampled is adjusted, it shifts the simulation to draw more samples from the interesting regions of the search space (Shortle & L'Ecuyer, 2011). If a uniform distribution is used, this degenerates to a generic Monte Carlo simulation.…”

Sensitivity analysis of rare-event splitting applied to cascading blackout models

“…This section describes the splitting methodology and notation used in this paper. For an introduction and overview of splitting, see L 'Ecuyer, Demers, andTuffin (2006), L'Ecuyer et al (2009) and Shortle and L'Ecuyer (2011).…”