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In statistics, the antithetic variates method is a variance reduction technique used in Monte Carlo methods. Considering that the error reduction in the simulated signal (using Monte Carlo methods) has a square root convergence, a very large number of sample paths is required to obtain an accurate result. The antithetic variates method reduces the variance of the simulation results. ==Underlying principle== The antithetic variates technique consists, for every sample path obtained, in taking its antithetic path — that is given a path to also take . The advantage of this technique is twofold: it reduces the number of normal samples to be taken to generate ''N'' paths, and it reduces the variance of the sample paths, improving the accuracy. Suppose that we would like to estimate : For that we have generated two samples : An unbiased estimate of is given by : And : In the case where ''Y''1 and ''Y''2 are independently and identically distributed, the covariance is zero and , therefore : The antithetic variates technique consists in this case of choosing the second sample in such a way that and are not iid anymore and is negative. As a result, is reduced and is smaller than the previous normal variance . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「antithetic variates」の詳細全文を読む スポンサード リンク
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