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Variance Reduction
Published in P. A. W. Lewis, E. J. Orav, Simulation Methodology for Statisticians, Operations Analysts, and Engineers, 2017
This chapter proceeds from the variance reduction techniques that are conceptually the simplest—antithetic variates and then control variables—to those that are conceptually quite difficult. Thus, the reader with less background might consider reading only through to Section 11.2, “Control Variables.” Control variables are likely to be the most useful of the variance reduction techniques because they can be applied to simulations of all aspects of the distribution of the response, and because controls are simpler to find than the characteristics required for other variance reduction techniques. Moreover, simulating a control variable, which must have a known or approximately known expectation, is invaluable for the all-important problem of validating the computer program that generates the simulation.
Monte Carlo Methods
Published in Matthew N.O. Sadiku, Computational Electromagnetics with MATLAB®, 2018
The term antithetic variates [28] is used to describe any set of estimators which mutually compensate each other's variations. For convenience, we assume that the integral is over the interval (0,1). Suppose we want an estimator for the single integral I=∫01g(U)dU
Development of fragility functions for rigid-frame bridges subjected to tsunami-induced hydrodynamic forces
Published in Structure and Infrastructure Engineering, 2022
Ismail M. I. Qeshta, M. Javad Hashemi, M. Reza Hashemi, Rebecca J. Gravina, Sujeeva Setunge
The selected samples for each random variable are randomly combined without replacement. In this combination, each representative sample for each random variable is considered in the analysis, only once. As a result, all possible ranges of the random variables are taken into account in the probabilistic model. The estimation accuracy of the probability of failure can be improved by using variance reduction methods. In this study, the Antithetic Variates (AV) technique (Ayyub & Haldar, 1984) is utilized in conjunction with the LHS to reduce the variance of the estimated value of the mean by introducing a negative correlation between different simulation cycles.