2023/24 ED560 statistics class

Welcome to the website of the 2023/24 ED560 statistics class!

Here below some important information concerning the class:

• Dates:   12-14 June 2024, 8-9 July; 9:30-12:30  and 14:00-17:00 

• Location:  Bat. Condorcet, salle 302 A

• Website of class on ED560 doctoral school page

Class contents:

• 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.

Recommended books:

• 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 

Class material, exercises and hands-on session code

• Material will be linked here once discussed in class

  • Lesson 1

  • Lesson 2

  • Lesson 3

  • Lesson 4

  • Lesson 5

• Exercises distributed in class.

  • Solutions to exercises

• 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

Roofit

• • 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

Roostats

• • 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