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Conclusion

Posted By: Maik Stiebler
Date: Monday, 15 August 2016, at 5:57 a.m.

In Response To: Conclusion (rambiz)

1. The "no bias" condition is equivalent to E(Y)=0. I don't think it is used anywhere in the derivation. When I state the condition for variance reduction to work, E(Y)=0 is tacitly assumed.

2. cor_(X,Y) is not fixed. It depends on which evaluation engine is used and which position is rolled out. After doing a rollout, the correlation can be estimated. At that point, it is a given, and you may want to choose sig_Y/sig_X so that variance reduction is maximised.

3. Yes, we can, unless I misunderstand our question.

4. I want to fine-tune the method to push down variance, nothing else. Now just doing a rollout and then rescaling your Y's after the fact to achieve sig_Y/sig_X=cor_{X,Y} might not be a good idea. It might even introduce some bias. I'm not sure. What you clearly could do is running a shorter probe rollout to find out estimates for cor_{X,Y} and the "original" sig_Y/sig_X, calculate an optimising scaling factor for Y and use that in the "real" rollout that follows. The question is if the gain in variance reduction is ever worth it.

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