# The likelihood confusion

Hi,

I have some confusions to understand the likelihood. Hoping someone can help me.

Suppose I have some data ( and it’s Gaussian distribution like mh ), I want to estimate the error of measure this mh. I find that in the RooFit manual, the example is something like 1) fitting the signal&background with Gaussian&Exp distribution, 2) Once the sigma and mu got, the -2Ln L got.
My confusion is that, my intuition is that the more data I have, the more accuracy I get. But in this way, if I have more data and the sigma&mu doesn’t change, I don’t get better accuracy, that’s why?

Another confusion comes from another way to calculate the Likelihood. L=f(x1,theta1)f(x2,theta2)… which x1, x2, represents the bin 1, bin 2 data ( simulated ) and theta1, theta2 represent the bin 1, bin 2 data ( observed ). This is assuming each bin is a Poisson distribution.
My confusion is that: suppose at first we have 20 bins and I get a 1-sigma limit when -2Ln L + 1 with some data x1, x2, x3,… , What happens if I consider one more bin, the L = L (with 20 bins) * f(the 21th bin), so in this case, the original 1-sigma limit is not the 1-sigma limit because now the the difference is not 1 but 1* f(the 21th bin).

In the end, if I have some mass distribution data, what is the best way to estimate the error of detect the mass ? ( the best mass, and the mass range in 1-sigma, 3-sigma… )

Hi,

I think the best is to look at some statistics book for HEP or follow some tutorial on statistics, like the CERN academic trainings that are recorded.

• more data you have will make the log-likelihood narrower and you will get smaller uncertainties, but the central values of the parameter will not change significatly

• The rule -2Ln L + 1 applies to likelihood ratio (log-likelihood differences) and not absolute likelihood values.
The likelihood values vary a lot experiment by experiment. See for example this notebook:
https://github.com/lmoneta/stat-course-ipmu/blob/master/Session2/LikelihoodAsGoF.ipynb

Lorenzo

This topic was automatically closed 14 days after the last reply. New replies are no longer allowed.