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.