Data analysis and modelisation

Description

Data analysis and modelling

• Basic concepts :
  • Definition of statistical and systematical uncertainties on measurements
  • Random variables, probabilities, momenta and probabilistic laws
  • Basic laws of random variables, the normal law and the central limit theorem
  • Application : counting rates, selection efficiency, estimation for means

• Combining uncertainties from measurements :
  • Joint probabilistic laws, covariance, correlation, the two-gaussians cases
  • Uncertainty propagation
  • Parameter estimation
  • Introduction to statistics
  • Basic methods : maximum likelihood (gaussian case, uncertainties, binned likelihood, extended likelihood), least squares (linear case, uncertainties, chi2 law)
  • Minimising methods

• Hypothesis testing :
  • Histogram fits
  • Tests : two and single hypothesis, power and error, p-value, the Neyman test, chi2-test , Kolmogorov-test

• Advanced estimation :
  • Interval estimation (confidence levels and intervals), low statistics, nuisance parameters
  • Dynamic estimation, Kalman filter

• Modelization :
  • Random number generation, Monte-Carlo techniques
  • Application to simulation, use cases with ROOT

• Advanced techniques :
  • Principle analysis components (PCA) and linear discriminant analysis (LDA)
  • Multivariate Analysis (MVA), artificial neural networks and decision trees

Compétences visées

•    Applying knowledge in physics

•    Apply methods from mathematics and digital technology

•    Produce a critical analysis, with hindsight and perspective

•    Interact with colleagues in physics and other disciplines

•    Develop and manage an experimental project, including digital aspects

•    Operate an experimental device, including digital aspects, from use to data analysis

•    Take on responsibilities in a team working on an experimental project

•    Research a physics topic using specialised resources

•    Communicate in writing and orally, including in English

•    Contribute to research work in physics

•    Respect ethical, professional and environmental principles in the practice of physics 

Bibliographie

 Books to be used as references 
• W.T.Eadie, D.Drijard, F.E.James, M.Roos, B.Sadoulet, Statistical methods in experimental physics, North Holland, Amsterdam and London, 1971. 
• J.R.Taylor, An introduction to Error Analysis University Science Books,1982 
• P.R.Bevington and D.K.Robinson, Data reduction and error analysis for the Physical Sciences McGraw-Hill Book Company,1969

 Textbooks 
• L.Lyons, Statistics for nuclear and particle physics Cambridge University press, New York, 1986 
• B.Escoubès, Statistiques et probabilités à l'usage des physiciens 1998 
• R.Früwirth, Data analysis techniques for high energy physics Cambridge university press, 2000 
• W.H.Hines, D.C.Montgomery, D.M.Goldsman, C.M.Borror, Probabilités et Statistique pour ingénieurs, Chenelière éducation, 2011

 Reviews and Briefbooks 
• the particle data group, Review of particle physics
• R.K.Bock, W.Krischer, The data analysis briefbook, Springer Verlag, 1998, 

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