Here below some important information concerning the class:
Dates: 8-12 June 2025; 9:30-12:30 and 14:00-17:00
Location: Bat. Condorcet, salle 302 A
The concept of probability and the most common probability laws (binomial, Poisson, exponential, Gaussian…)
Parameter estimation: the method of moments, the Maximum Likelihood method, the chi-square estimator
Confidence intervals
Test of hypotheses: simple hypotheses, goodness of fit
The Bayes rule, the Bayesian approach to parameter estimation
Several practical examples will be presented and hands-on tutorial sessions will be proposed.
R. Barlow, Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences - Wiley - beginners level
F. James, Statistical Methods In Experimental Physics (2nd Edition) - World Scientific - classic book
L. Lista, Statistical Methods for Data Analysis in Particle Physics (2nd Edition) - Springer - modern, concise yet complete
G. Cowan classes, in particular the one on LS
Exercises distributed in class.
Hands-on session: code is based on CERN ROOT. Mini tutorial is here. Introduction slides are available here.
Below the list of directories containing the exercises. In each directory <alpha>you will find several files, depending if the example is written in ROOT (<alpha>.C) , in pyROOT (<alpha>.py ), in a ROOT jupyter notebook (<alpha>.ipynb), or in a pyROOT jupyter notebook (py_<alpha>.ipynb). Select the 'flavor' you prefer.
To run the ROOT version:
root [0] .L <macro_name.C>
root [1] macro_name(<insert here>, <possible parameters>, <if needed>)
To run the pyROOT version:
>>> import <alpha>
>>> alpha.alpha(<insert here>, <possible parameters>, <if needed>)
For the jupyter notebooks:
$ jupyter notebook
runArgusModel - example from website; sig+bkg pdf, generate data and fit --> exercise: change pdf
RooWorkspaceExample - example on how to use factory mode --> exercise: try to save to file and retrieve
RooConvolution - an example of convolution --> exercise: try to change the sigma value (sl) and see what happens
plotData - an example to read data (it requires: myWorkspace_with_data.root) --> exercise: try to fit data building a signal + background model, estimating signal and background yields
Priors - for counting experiment comparison of posterior depending on prior's choice
Priors_with_bkg - for counting experiment comparison of posterior depending on prior's choice this time with background
The examples below require this root file.
exercise_0 - Fit a lower statistics data sample using RooFit - ex: INFNStatRooStats2017
exercise_1 - Compute the excess significance - same reference as above
exercise_2 - Compute upper limits to the signal yield using frequentist and Bayesian methods - same reference as above
exercise: check if there is an excess at 105 GeV/c^2 in the invm spectrum in this file
hint: use the macro in plotData to plot again the spectrum