Maximum likehood unleashed!

[Boud Roukema]

Thanks Micha³,

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¶æ
Boud