Description

Data analysis and modelisation

• Basic concepts :
  • Definition of statistical and systematical uncertainties on measurements.
  • Random variables, probabilities, momenta and probabilistic laws.
  • Three 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.
  • Application : combining measurements of the same quantity and some practical examples.

• Parameter estimation :
  • Introduction to statistics.
  • Basic methods : maximum likelihood (the gaussian case, uncertainties, binned likelihood, extended likelihood), least squares (linear case, uncertainties, chi2 law).
  • Minimizing methods.

• Hypothesis testing :
  • Histogram fits.
  • Tests : two and single hypothesis, power and error, p-value, the Neyman test, chi2-test , Kolmogorov-test.
  • Application : histogram comparison, Higgs search at LEP.

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

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

• Advanced techniques :
  • principle analysis components (PCA) for complex ensemble.
  • Multivariate Analysis (MVA), Fisher discriminants, artificial neural networks, decision trees.

Contacts

Responsable(s) de l'enseignement

• Boris Hippolyte

MCC

Les épreuves indiquées respectent et appliquent le règlement de votre formation, disponible dans l'onglet Documents de la description de la formation.

Régime d'évaluation

CT (Contrôle terminal, mêlé de contrôle continu)

Coefficient

2.2

Évaluation initiale / Session principale - Épreuves

Seconde chance / Session de rattrapage - Épreuves