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BGonline.org Forums
Further reading: Control variates
Posted By: Maik Stiebler In Response To: Further reading: Control variates (rambiz)
Date: Thursday, 18 August 2016, at 7:20 p.m.
They do lead to the same result, right? My optimizing condition was sig_Y/sig_X=cor_{X,Y} or equivalently sig_Y=cor_{X,Y}sig_X, Wikipedia says c*=-cov_{X,Y}/var_Y, which equals -cor_{X,Y}sig_X/sig_Y, so -c*sig_Y=cor_{X,Y}sig_X. c* was not explicitly mentioned in my formulas, but hinted at in the text, and the difference in signs is due to different formulations of the method.
How is Var(m*)=Var(m)+c^2Var(t)+2cCov(m,t) minimized? Just find the c that lets the derivative with respect to c, i.e. 2*cVar(t)+2Cov(m,t), equal zero.
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