Thanks Micha�,
On 3 Jun 2002, Michal Frackowiak wrote:
I am sending a short theory behind max. likehood method and its adaptation in comparing curves with given errors. I believe this will be helpfull - it seems to me as the best way that does the trick:
- it takes particular errors into account
- lets you estimate errors of the fit
- as well as contours of confidence when making a grid.
It's a nice explanation.
This is well tested in my own soft so I hope should work in this case as well. In case of questions - I would be even more than glad to help.
Well, although it's clear the method can give a result, for it to give a correct result, the different r values would need to be independent from one another.
So I see three problems, 2 easily solvable, 1 more fundamental:
- solvable: (1) If we combine all three: L_{12} L_{23} L_{13} then one of these three is dependent on the other two. So it seems to me that we have to (arbitrarily) remove one of the three, even though it's clear that this is an arbitrary choice.
(2) There is some smoothing in the curves output by DEplotcorrnall. This can be removed (just set ismoo=0 on line 283 of DEplotcorrnall in DE-V0.04, I think this should be OK), but then my worry is that the result will be extremely noisy. An alternative solution would be to to only test one out of every (ismoo+1) values of r .
- fundamental: (3) Different bins in a correlation function depend on one another. A single quasar is a member of many pairs, and different pairs fall into different bins. So the different r values in a single function zeta(r) depend on one another.
So for this reason I find it hard to believe that L (rescaled) would be a true probability density function.
It's certainly a good idea, so I'll put it as one of the DEplot_cf tests, but I don't think it'll give true error bars.
Cze�� Boud