| |
BGonline.org Forums
Calculating confidence values
Posted By: Timothy Chow In Response To: Calculating confidence values (Maik Stiebler)
Date: Sunday, 30 August 2009, at 6:22 p.m.
Bob Koca wrote:
I would like to introduce variance reduction back into the picture.
Maik Stiebler already answered this; I would just add the general remark that variance reduction amounts to collecting more information about the position than the raw outcome. So the Bayesian philosophy would be: Figure out what random variable you're estimating (in the case of variance reduction, this might be a luck estimate of some sort), write down prior probabilities for the values it could take, and update those probabilities according to the evidence you accumulate. This might mean keeping around an extra array or two to track the extra random variables, but you can always do it, in principle.
Maik Stiebler wrote:
Is the beauty of the approach then only that we can incorporate a fancy prior, or will the result of the confidence value that we get with a uniform prior be noticably different from what we can compute with the usual shortcut via jsd's?
I hesitate to guess how different the answer will be without doing some further estimates or calculations. But if your real question is what the Bayesian approach buys you, I would say that it gives you a conceptually simple way to calculate other quantities of interest. I already mentioned the example of comparing multiple plays. Suppose you want to know, "What is the probability that the equity of Play A is at least 0.050 greater than that of Play B and at least 0.100 greater than that of Play C?" It's a little tricky to figure out what the null hypothesis should be here under the usual approach, but in the Bayesian approach it's clear which array entries you need to sum up. The reason the Bayesian framework is easier to work with (I claim) is that it more closely tracks what our intuition expects the statistics to tell us.
| |
BGonline.org Forums is maintained by Stick with WebBBS 5.12.