Efficiency improvement techniques

Abstract

This paper provides an overview of the five most commonly used statistical techniques for improving the efficiency of stochastic simulations: control variates, common random numbers, importance sampling, conditional Monte Carlo, and stratification. The paper also describes a mathematical framework for discussion of efficiency issues that quantifies the trade-off between lower variance and higher computational time per observation.

Efficient simulation of blackout probabilities using splitting

“…There are two main approaches that have been used to improve the efficiency of rare-event simulations: Importance sampling and splitting (e.g., [21]). The idea of importance sampling (e.g., [13,15]) is to change the sampling distribution so that rare events are more probable. For example, Bae and Thorp [2] use importance sampling to study hidden failures in a power grid.…”

Efficient Splitting Simulation for Blackout Analysis

“…After , , and are determined in Phases 1 and 2, the optimal efficiency problem in (1) can be simplified as follows: (6) where is the computing budget already used in the pilot simulation in Phase 1. Let be the number of split simulation replications (or runs) for stage , let be the fixed number of simulation runs that successfully reach level , and let be the average one-run simulation cost for stage .…”

“…The two main approaches to rare event estimation are importance sampling and splitting. Importance sampling [6] works by appropriately changing the sampling distribution to make the rare event more probable, and thus easier to estimate, then re-scaling the result to recover the correct probability. The main limitation is that this usually requires specific knowledge about the problem, so solutions tend to be highly sensitive to the assumptions of the model.…”

Estimating small cell-loss ratios in ATM switches via importance sampling

“…For general background on efficiency improvement (or variance reduction), we refer the reader to Bratley et al [1987], Fishman [1996], Glynn [1994], and L'Ecuyer [1994]. IS is well explained in Glynn and Iglehart [1989], Shahabuddin [1994], Heidelberger [1995], Sadowsky [1996], and the several other references given there.…”