Proper calculation of the efficiency

[Silviu]

Homework Statement

Hello! This is actually a computational-statistics problem in data analysis, and I got a bit stuck. I have several events from a Monte Carlo simulation from 2 particles collision and for each event I have the primary vertex and the tracks associated to it. I wrote an algorithm which, given the tracks (and their parameters) reconstructs the primary vertex (PV). I want to calculate the efficiency of the algorithm (so the number of reconstructed PV vs the number of actual PV) in bins of number of tracks. I attached a plot I obtained. The 3 colors represent the threshold for the energy of the tracks I used to reconstruct the primary vertex (the minimum energy needed by a track). My professor said that I should also think about the probability of getting a given number of tracks with a given energy. For example, we get to 90% with 5 tracks above 10 GeV but we need 20 above 3 GeV for the same efficiency. However, the probability of getting a vertex having 3 tracks with 3GeV associated with it is different than the probability of having a vertex with 20 tracks with 10GeV. So, should I take this into account and weight somehow my histogram using that information? And if so, how should I do it? I am not sure how to account for the probability of getting a certain number of tracks associated with a certain vertex. Thank you!

Homework Equations

The Attempt at a Solution

 

[Nate810]

Yes, you should take this into account and weight your histogram. The probability of getting a certain number of tracks associated with a certain vertex is determined by the probability density function (PDF) that describes the distribution of the events. By using this PDF, you can calculate the probability of finding a certain number of tracks with a certain energy for each event in the Monte Carlo simulation. This will allow you to weight the data in the histogram based on the likelihood of obtaining that particular combination of tracks and energies. You can then use the weighted data to calculate the efficiency of the algorithm.