# Likelihood vs Chi2 fit

Using Roofit, I tried to fit a binned distribution (with thousands of events), with chi2 as well as likelihood fit,
why they give quite different answers (about 3% change) ?

(1) With unbinned fit to same distribution, I got parameter value 1.478
(2) With 100 bins, likelihood fit i also got 1.478
(3) as i decrease the bin# to 10bins…the parameter value increases to 1.51.
(4) However with same 10 bins, the chi2 fit gives me 1.478…

Can you suggest whats going on ?

-Sanjay

Hi,

I would be interested to see what is the result if you use a binned likelihood fit using ROOT instead of RooFit.
If the distribution the bin content is a Poisson, the Likelihood fit should give you the correct un-biased result. However, since you might have large bin, it is possible that effect cause by computing the p.d.f. at the bin center instead of using its integral can bias the result.

The chi2 fit should be used only when the bin distribution is normal (i.e. in case of very large statistics). however since you don’t know the true sigma in each bin, this will make always the histogram fit biased.

Best Regards

Lorenzo

The Binned Likelihood fit (with 10 bins) with ROOT gives same as chi2 fit in ROOT. I tried binned likelihood fit with bin center and bin integration , both options, they give pretty much similar results…

I am just curious if there is any thing to do to get 1.478 paramter value with binned likelihood fit using RooFit (any correction or scaling…or other options) …

-Sanjay

Hi ,

I would need your program to understand. But I suspect is caused by a known problem (bias) in the binned likelihood fit of RooFit. I have already seen something similar in the past.
See for example this open issue in JIRA
https://sft.its.cern.ch/jira/browse/ROOT-3874

Lorenzo

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