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Science Forum Index » Statistics - Math Forum » Maximum Likelihood threshold
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| Guest |
 Posted: Thu Apr 24, 2008 4:44 am |
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Dear all,
I'm an astrophysicist and I'm working with a code computing the
maximum likelihood of finding a galaxy cluster in a certain point of
the sky given a model and a distribution of galaxies. I would like to
find a treshold that corrisponds to a N-sigma detection...is it
possible to define it statistically? I mean, does it exist something
equivalent t the chi square distribution for the maximum likelihood,
that translate a certain likelihood value in a "confidence limit"?
Thanks!
cheers
Stefania |
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| David Jones |
| Posted: Fri Apr 25, 2008 7:30 am |
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Guest
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stefania.giodini@gmail.com wrote:
Quote: Dear all,
I'm an astrophysicist and I'm working with a code computing the
maximum likelihood of finding a galaxy cluster in a certain point of
the sky given a model and a distribution of galaxies. I would like to
find a treshold that corrisponds to a N-sigma detection...is it
possible to define it statistically? I mean, does it exist something
equivalent t the chi square distribution for the maximum likelihood,
that translate a certain likelihood value in a "confidence limit"?
Thanks!
cheers
Stefania
You may be able to base something on a likelihood ratio test if you can pose your problem in a suitable way. The twice the log-likelihood-ratio has an approximate chi-squared distribution as you note, so that any "points" or models that are not rejected by a corresponding significance test can be used to define a confidence region.
David Jones |
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| Guest |
| Posted: Mon Apr 28, 2008 10:22 pm |
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Thanks David, you're right, I converted my problem in log likelihood
ratio and that is more handy...but the chi-square approximation works
in the N->infinity case (N is the number of points on which I compute
the likelihood) and I'm not really in this case...some area of the sky
have 10-20 or less points...should I use Cash-statistics there? In
this case does someone knows where to find a critical value table on
the web? (not succeded until now...)
Cheers&Thanks
Stefania
On 25 Apr, 14:30, "David Jones" <dajx...@ceh.ac.uk> wrote:
Quote: stefania.giod...@gmail.com wrote:
Dear all,
I'm an astrophysicist and I'm working with a code computing the
maximumlikelihoodof finding a galaxy cluster in a certain point of
the sky given a model and a distribution of galaxies. I would like to
find a treshold that corrisponds to a N-sigma detection...is it
possible to define it statistically? I mean, does it exist something
equivalent t the chi square distribution for the maximumlikelihood,
that translate a certainlikelihoodvalue in a "confidence limit"?
Thanks!
cheers
Stefania
You may be able to base something on alikelihoodratio test if you can pose your problem in a suitable way. The twice the log-likelihood-ratio has an approximate chi-squared distribution as you note, so that any "points" or models that are not rejected by a corresponding significance test can be used to define a confidence region.
David Jones |
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| David Jones |
| Posted: Tue Apr 29, 2008 4:52 am |
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Guest
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stefania.giodini@gmail.com wrote:
Quote: Thanks David, you're right, I converted my problem in log likelihood
ratio and that is more handy...but the chi-square approximation works
in the N->infinity case (N is the number of points on which I compute
the likelihood) and I'm not really in this case...some area of the sky
have 10-20 or less points...should I use Cash-statistics there? In
this case does someone knows where to find a critical value table on
the web? (not succeded until now...)
Cheers&Thanks
Stefania
Well I found "Cash-statistics " at http://avalon.star.le.ac.uk/sherpabeta/statistics/ , which suggests that the chi-squared approximation is OK and that the log likelihood ratio and "Cash-statistics " are equivalent. If in doubt about the validity of the approximation, you could do some simulations from your model to test it.
For on-line stuff see the end of (ie under External links) http://en.wikipedia.org/wiki/Chi-square_distribution
David Jones |
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| Herman Rubin |
| Posted: Tue Apr 29, 2008 10:46 am |
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In article <4816efe0$1@news.nerc-wallingford.ac.uk>,
David Jones <dajxxxx@ceh.ac.uk> wrote:
Quote: stefania.giodini@gmail.com wrote:
Thanks David, you're right, I converted my problem in log likelihood
<> ratio and that is more handy...but the chi-square approximation works
<> in the N->infinity case (N is the number of points on which I compute
<> the likelihood) and I'm not really in this case...some area of the sky
<> have 10-20 or less points...should I use Cash-statistics there? In
<> this case does someone knows where to find a critical value table on
<> the web? (not succeded until now...)
<> Cheers&Thanks
<> Stefania
With your sample size, it might be possible to determine
the probability exactly, or use simulation. I do not
see that any version of the chi-squared approximation
can be used with such small sample sizes.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 |
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