EC
Data analysis and modelisation
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.