1. Statistical Methods for Data Analysis Introduction to the course Luca Lista INFN Napoli

2. Luca ListaStatistical Methods for Data Analysis2 Purpose of the course Provide concepts and tools to perform statistical experimental data analysis Most of the examples are taken from High Energy Physics (HEP)… –…but the scope of the presented methods is not necessarily limited to the HEP field –Several students of paste editions of this course successfully applied those methods to other fields

3. Luca ListaStatistical Methods for Data Analysis3 Topics covered Statistics and probability distributions –Mainly intended as a reminder, assuming most of the concepts are already known –Frequentist vs Bayesian probabilities Bayes theorem and Bayesian approach Random numbers and Monte Carlo Parameter estimates –(Extended) Maximum Likelihood (ML) and least  2 fits –Confidence intervals and coverage problems –Fit quality with Toy Monte Carlo Upper limits estimates –With a bit of history up to the recent ‘trends’ Introduction to multivariate discriminators –Likelihood ratio, Fisher classifier –Neural Networks, Boosted decision trees

4. Luca ListaStatistical Methods for Data Analysis4 Recent statistics developments The availability of cheap CPU allows to adopt strategies that were unpractical up to ~15 years ago: –More complex fits –Large ‘Toy Monte Carlo’ production More emphasis is put on evaluating carefully the correct interpretation and statistical properties of the adopted estimators –Frequentist vs Bayesian approach (Pseudo)frequentist evaluation of upper limits estimators –Standardized for Higgs search at LHC –Developed for LEP Higgs working group: ‘CL s ’ method, Feldman- Cousin ‘unified’ approach More standardized tools, and ability to share results –ROOT, RooFit, RooStat, TMVA –Problem sometimes shifted from finding the correct statistical solution to find the right (and working…) implementation within the ‘standard’ tools

5. Luca ListaStatistical Methods for Data Analysis5 Recommended toolkits ROOT –General purpose data handling and visualization –Tools for basic statistic problems: random number generators, basic fitting RooFit –PDF modeling, fitting (in particular, ML), Toy Monte Carlo TMVA –Multivariate analysis –Simultaneous comparison of different classifiers Other tools are also available on the market, but I’m not an expert user of other products

6. Luca ListaStatistical Methods for Data Analysis6 Credits Wouter Verkerke –For RooFit tutorials and examples –Many of the RooFit slides are taken from his presentations Bob Cousins –For reading the slides and providing useful suggestions –“I could tell from your lectures that you like to think in detail and depth about these things”

7. Luca ListaStatistical Methods for Data Analysis7 References