Control variates: Difference between revisions

→‎Underlying principle: added note on extensions of method
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(→‎Underlying principle: added note on extensions of method)
In the case that <math>\textrm{Cov}\left(m,t\right)</math>, <math>\textrm{Var}\left(t\right)</math>, and/or <math>\rho_{m,t}\;</math> are unknown, they can be estimated across the Monte Carlo replicates. This is equivalent to solving a certain [[least squares]] system; therefore this technique is also known as '''regression sampling'''.
When the expectation of the control variable, <math>\mathbb{E}\left[t\right]=\tau</math>, is not known analytically, it is still possible to increase the precision in estimating <math>\mu</math> (for a given fixed simulation budget), provided that the two conditions are met: 1) evaluating <math>t</math> is significantly cheaper than computing <math>m</math>; 2) the magnitude of the correlation coefficient <math>|\rho_{m,t}| </math> is close to unity. <ref name="varred17"/>
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