This is an unfolding exercise for the "Statistical Data Analysis" course.

You get two datasets

A sample of cosmic-ray events

• For each event you have a measurement of its rigidity (= momentum/charge)
• You have a MC simulation sample with 5x more events where for each event you have both "generated" and "measured" rigidity
• You should unfold the rigidity distribution and reconstruct the flux (a histogram with the geomagnetic transmission function is also provided)
• Fit the spectrum with the function in the slides and measure both the spectral index and its change

You also have a small code sample that opens the root files and extract the TTree objects setting up the branches, and provides a suggestion for the histogram binning (beware of non-uniform bins and their effect in some of the unfolding procedures!!!).

A sample of muon pairs from some beam collisions

• For each event you have the 4-momentum of each muon
• You have a MC simulation sample with 10x where for each event you have both "generated" and "measured" 4-momenta
• You should unfold the invariant mass distribution
• Fit the peak in the mass distribution with a gaussian function (beware of the background) and measure its position, its width, and the total number of events associated to it.

You also have a small code sample that opens the root files and extract the TTree objects setting up the branches

For each dataset choose TWO METHODS from:

• Iterative correction factor
• Regularized SVD
• Bayesian (bonus points if improved)
• Forward folding

and compare the results you get with each method.