How to extract the error from two dimensional contour plot?


I need to extract the uncertainty from a two-dimensional chi square minimization contour plot between the three variables (x, y, and z). Basically, I plotted the two physical parameters on the x and y axes and the chi square on the z axis. I obtained a closed contour (chi square minimization condition). Now, based on that closed contour, I want to extract the uncertainty in two physical parameters (x and y). How do I extract it? Please let me know if anyone has any ideas.

Hi and welcome to ROOT!

I think @moneta and @jonas will be able to help you. In principle, what you are after is a “section” along 2 directions of the 2D shape of your chi2 I believe…



From the contours of the chi2 function you can get the confidence interval regions of your two variables x and y. If you want the separate uncertainty in x and y you should do a profile likelihood scan (or MINOS error analysis). See for example this note and any statistical book for HEP, such as this one (see chapter 2).


Thank you for sharing the information.

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