Slicing the chi-square m-parameter hyper-surface to 2D

Hello,

I’m minimizing Chi-square value with a grid search in m-dimensional space;

a nice 2D example is shown (muonfit )

What I need is a slice of this hyper-surface in 2D (for two chosen parameters);

Is there a good way of doing this in ROOT plus making the corresponding constant chi-square contours for this,

thanks, Damir

Hi,

Do you have the grid values of the chi2 for the two chosen parameters keeping the other fixed ?
If this is the case you can use methods of the TH2 or TGraph2D painter classs for finding the contours.

Lorenzo

No; its a hyper-surface…Chi-square is a function of all sampled m-parameters;

From your answer the slicing then is not obvious,

Damir

No it is not obvious, you need to decide exactlly what you want.
You have chi2(x1,…xN)
and you can have:

  • chi2(x1,x2) keeping all the other parameter fixed. But for which values ? Their values for which chi2 has a minimum ?
  • a profile of chi2(x1,x2) , which means for each x1 and x2 you find the minimum of the chi2(x3,…xn). This is the algorithm used in Minuit/Minos for finding the contours
  • Marginalize the chi2 distribution by computing the Integral(chi2(x1,…,xn)dx3,…dXn)

Then for computing the chi2 function from the data points you can use a machine learning regression algorithms

Lorenzo

sure; This is correct,

I’m doing now = chi2(x1,x2) keeping all the other parameter fixed + Their values for which chi2 has a minimum.

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