Antithetic variates (source code)

= Antithetic variates
{wiki}

<Antithetic variates> deliberately couple <unbiased estimators> of the same <expectation> with negative <covariance>. Their average can have smaller <variance> than an average using independent draws. For example, evaluating a monotone integrand at $U$ and $1-U$, where $U$ has a <uniform distribution>, gives opposite fluctuations while preserving both marginal distributions.