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ROOT Statistics Classes

Classes for Computing Limits and Confidence Levels

A new package, RooStats, provides the advanced functionality for computing limits and confidence levels with the recommended statistical tools.
Dedicated classes exist also for some particular cases:

  • TFeldmanCousins class calculates the CL upper/lower limit for a Poisson process using the Feldman-Cousins method (as described in PRD V57 #7, p3873-3889).
  • TRolke computes confidence intervals for the rate of a Poisson process in the presence of background and efficiency. It uses the profile likelihood technique for treating the uncertainties in the efficiency and background estimate.
  • TLimit class computes 95% C.L. limits using the Likelihood ratio semi-Bayesian method (see e.g. T. Junk, NIM A434, p. 435-443, 1999).

Fitting Classes

Classes for fitting exist in the MathCore library and they are used to fit in ROOT the data objects like histograms, trees and graphs.
For complex fitting and data analysis modeling, the toolkit RooFit is available in ROOT (see the RooFit User Guide).
Specific classes exist for some particular fitting problems:

  • TFractionFitter fits Monte Carlo (MC) fractions to data histogram (a la HMCMLL, R. Barlow and C. Beeston, Comp. Phys. Comm. 77 (1993) 219-228), taking into account both data and Monte Carlo statistical uncertainties.
  • TMultiDimFit implements multi-dimensional function parameterization for multi-dimensional data by fitting them to multi-dimensional data using polynomial or Chebyshev or Legendre polynomial.
  • TSpectrum contains advanced spectra processing functions for 1- and 2-dimensional background estimation, smoothing, deconvolution, peak search and fitting, and orthogonal transformations.
  • TSPlot - to disentangle signal from background via an extended maximum likelihood fit and with a tool to access the quality and validity of the fit producing distributions for the control variables. (see M. Pivk and F.R. Le Diberder, Nucl. Inst. Meth.A 555, 356-369, 2005). A new SPlot class using RooFit, RooStats::SPlot,is provided also by the RooStats package.
  • TBinomialEfficiencyFitter to calculate a selection's efficiency from two histograms, one containing all entries, and one containing the subset of these entries that pass the selection.

Multi-variate Analysis Classes

TMVA is the reccomended package for multivariate data analysis in ROOT (see the User’s Guide).
ROOT provides in addition some specific multi-variate classes:

  • TMultiLayerPerceptron is a Neural Network class, which can be used for classification or for regression analysis.
  • TPrincipal provides the Principal Component Analysis.
  • TRobustEstimator is a robust method for Minimum Covariance Determinant Estimator (MCD).