Jason House wrote:
On Dec 6, 2007 11:38 AM, Rémi Coulom <[EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]>> wrote:Jason House wrote: > > This may serve as a good test of if there is enough data to assign > values to the patterns. I did not mention this in my paper, but you can rather easily estimate uncertainty margins around Elo values. This involves computing the second-order derivative of the probability distribution with respect to log(gamma). Since the distribution has a shape that looks very much like a Gaussian, the second-order derivative at the maximum is a good estimation of -1/sigma². That is how I compute confidence intervals in bayeselo.What do you mean by the probability distribution with respect to log(gamma)? Do you mean a plot of the prediction rate with only the gamma of interest varying?
No the prediction rate, but the probability of the training data. More precisely, the logarithm of that probability.
If you have P(x)=A*exp(-x²/2sigma²), then log(P(x))=log(A)-x²/2sigma², and d²(log(P(x)))/dx²=-1/sigma². This means that, for a Gaussian probability distribution, the second-order derivative directly gives the variance. For distributions that look similar to a Gaussian, the second-order derivative is a good approximation.
Rémi _______________________________________________ computer-go mailing list computer-go@computer-go.org http://www.computer-go.org/mailman/listinfo/computer-go/
