Re: Maximum likelihood estimator and multiple maxima

Hello Alejandro,

Are you at liberty to disclose the formula for the model,
and perhaps also the data? I'd like to take a look for myself,
maybe others will too.

> nasty results in regards to confidence intervals for some parameters.
> Either using the Fisher matrix or a gaussian approximation,
> I get huge, unphysical figures for the uncertainty of beta.

Well, an approximation which assumes a Gaussian distribution
is valid only to the extent that the distribution in question is
Gaussian.
>>From what you've written, the distribution is very far from Gaussian.

> This has been striking because a simpler cosmological model
> that I have investigated time ago, with good fitting behavior, has
> precisely beta as relevant parameter and four of the parameters
> of the present model set to zero.

Let's see, that's five parameters. What about the sixth one?

> So I went to the larger data set (N=157) with the hope that it
> would cure the problem. Clearly this expectation was wrong.
> But could it be that a much larger data set does generate a
> nicely behaved likelihood? The issue is relevant as much
> larger data sets are expected to be obtained in the near future
> for this particular kind of astronomical observations.

More data could help, but there's no guarantee.
In particular, if the model has multiple maxima of likelihood
due to symmetry, or maxima which are lines or surfaces due
to redundant parameters, those will be present no matter how
many data or how few.

Like everyone else here, I'm guessing about what might be
happening -- if you can show us the model formula and the data,
it might be possible to make definite statements.

Hope this helps. It's a very interesting problem. Good luck,

Robert Dodier

.

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