Re: [Bug-gnubg] Formula for standard error?

[nis]

On 16 Aug 2002 at 17:31, Joern Thyssen wrote:

> On Fri, Aug 16, 2002 at 05:25:51PM +0200, address@hidden wrote
> > Hello
> > 
> > Can anyone enlighten me as to the formula used for calculating 
> > standard error for the rollouts? I can't get it to match with any of 
> > the formulas I have found. Specifically, I would expect it to be:

> > sqrt(Variance(outcome)/(n)) 


> line 874 in rollout.c:
> 
> aarSigma[ ici ][ j ] = sqrt( aarVariance[ ici ][ j ] / ( i + 1 ) );
> 
> aarVariance is calculated iteratively using formula (53) on

And in that calculation lies the error. This formula:   
                
           aarVariance[ ici ][ j ] =
               aarVariance[ ici ][ j ] * ( 1.0 - 1.0 / ( i + 1 ) ) +
         ( i + 2 ) * rDelta * rDelta;

Should read 

           aarVariance[ ici ][ j ] =
               aarVariance[ ici ][ j ] * ( 1.0 - 1.0 / i ) +
         ( i + 1 ) * rDelta * rDelta;

The confusing part is of course the zero-based loop - but this 
cancels out with the fact that the formula given is for the (j+1)th 
"partial variance".
-- 
Nis Jorgensen
Friends Development & Support
Greenpeace 
+31 (20) 52 36 202