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Control variates

The control variates method is a variance reduction technique used in Monte Carlo methods. It exploits information about the errors in estimates of known quantities to reduce the error of an estimate of an unknown quantity. The control variates method is a variance reduction technique used in Monte Carlo methods. It exploits information about the errors in estimates of known quantities to reduce the error of an estimate of an unknown quantity. Let the unknown parameter of interest be μ {displaystyle mu } , and assume we have a statistic m {displaystyle m} such that the expected value of m is μ: E [ m ] = μ {displaystyle mathbb {E} left=mu } , i.e. m is an unbiased estimator for μ. Suppose we calculate another statistic t {displaystyle t} such that E [ t ] = τ {displaystyle mathbb {E} left= au } is a known value. Then is also an unbiased estimator for μ {displaystyle mu } for any choice of the coefficient c {displaystyle c} . The variance of the resulting estimator m ⋆ {displaystyle m^{star }} is

[ "Hybrid Monte Carlo", "Monte Carlo molecular modeling", "Monte Carlo method in statistical physics" ]
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