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Calculating confidence values

Posted By: Maik Stiebler
Date: Sunday, 30 August 2009, at 7:33 a.m.

In Response To: Calculating confidence values (Bob Koca)

There are two ways you could do it.

I think the first way you describe (store only the absolute equity of each play) is used in gnubg (and all other bots, as far as I know). It would be best to have both informations (you could also store them in a neat covariance matrix, if you have more than two plays to consider). On the other hand, I believe covariance is usually negligible when VR is used.

I would like to introduce v ariance reduction back into the picture. Suppose the variance reduced result is 60% win chance for a play. How would you update?

Then we multiply the value of A[i] with the probability that the varianced result is 60% if the true value of the equity were i/1000. For that we need a prior assumption about the variance that is left in there by variance reduction. This assumption can be simple (just guess a prior value of the variance and use it), or more complex, in which case you could use a prior distribution for the variance as well, in which case you would not only have a list A for play A, but a list of lists A1, A2, A..., An, where each list in the list is updated under the assumption of a list-specific variance). I guess a good practical third way would be to estimate the variance in the normal un-Bayesian way and then do the Bayesian updates of the equity distribution with that estimated value.

How long would it take for the Bayesian updating to give that result? I think that most of the advantage of VR vanishes.

Not at all, if the variance is estimated well.

@Timothy: Assuming DMP, no VR, enough trials for the posterior to resemble a normal distribution, no correlation between the equities of play A and B. 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?

Messages In This Thread

• Calculating confidence values
  Timothy Chow -- Sunday, 30 August 2009, at 12:47 a.m.
  • Calculating confidence values
    Bob Koca -- Sunday, 30 August 2009, at 2:08 a.m.
    • Calculating confidence values
      Maik Stiebler -- Sunday, 30 August 2009, at 7:33 a.m.
      • Calculating confidence values
        Timothy Chow -- Sunday, 30 August 2009, at 6:22 p.m.
        • Calculating confidence values
          Maik Stiebler -- Tuesday, 1 September 2009, at 12:15 p.m.
  • Calculating confidence values
    Tom Keith -- Sunday, 30 August 2009, at 2:24 p.m.
    • Calculating confidence values
      Maik Stiebler -- Sunday, 30 August 2009, at 3:02 p.m.
      • Calculating confidence values
        Tom Keith -- Monday, 31 August 2009, at 1:27 p.m.
        • Calculating confidence values
          Maik Stiebler -- Tuesday, 1 September 2009, at 11:57 a.m.
    • Calculating confidence values
      Timothy Chow -- Sunday, 30 August 2009, at 6:40 p.m.
      • Calculating confidence values
        Maik Stiebler -- Tuesday, 1 September 2009, at 11:48 a.m.
        • Calculating confidence values
          Timothy Chow -- Wednesday, 2 September 2009, at 4:33 a.m.