Variates, antithetic

Hammersley JM, Morton KW. 1956. A new Monte Carlo technique antithetic variates. Proc Cambridge Philos Soc 52 449-475. 

Other devices for improving the efficiency of the sampling techniques in Monte Carlo calculations are Russian roulette and splitting described by Kahn [4], the conditional Monte Carlo of Trotter and Tukey [6], and the antithetic variates of Hammersley and Morton [7 8]. It is likely that further powerful techniques of this sort await discovery, whereby the usefulness of Monte Carlo for practical problems may be greatly extended. 

Among variance reduction techniques the importance sampling technique is most frequently applied in structural reliability analysis e.g. in [1,3,10-12] whereas other techniques e.g. stratified sampling [13], Latin hypercube sampling [14,15] and antithetic variates [11], also proved to be very powerful tools for structural reliability analyses. The concepts of these techniques will be discussed briefly below. 

Recall that Eq. 14 provided an estimate for the variance Pf. Using the so-called variance reduction techniques, it is possible to reduce this variance and thereby obtain an improved estimate of Pf. Such techniques are called variance reduction techniques (Kalos and Whitlock 2008) and are commonly used while estimating Pf. One such technique is popularly called the conditional expectation method in this method, a control variable is selected and the variance of Pf is reduced by removing the random fluctuations of this control variable which was not conditioned. In another technique, popularly known as the technique of antithetic variates, negative correlation is purposefully induced between successive samples to decrease the variance of the estimated mean value. It is also common to use the technique of antithetic variates in combination with the conditional expectation method (Haidar and Mahadevan 2000). 

The concrete engineer should be cognizant of the effects of a mixture of admixtures - the incremental effects at higher dosages, the interactive, antithetical or synergistic effects, variation with different cement brands, ambient temperature and water-cement ratios - so that preventive or compensatory action can be taken. Some of the important points to be considered are as follows ... 

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