[ROOT] multidimensional/multicorrolated/multiconstrained fit

From: schulte-wissermann (schulte@pktw09.phy.tu-dresden.de)
Date: Sat Nov 06 2004 - 23:06:15 MET


hi all ROOTers,
 consider the following problem:
  - you have a signal (e.g. missing-mass-spektrum) which is 
    parameterized by a Lorentz convoluted with a Gaus. 
    the signal is on some kind of background wich you emulate by a 
    cubic function. after the fit i get as a result (let's say) seven 
    parameters.

    NO PROBLEM SOFAR: see the famous FittingDemo and langaus tutorials.

    now the problem:
     i now split my data considering another observable (let's say ten 
     missing-mass distributions as a function of an angle of an ejectile).
     i now have to fit ten INDIVIDUAL histos, however physics tells me 
     that the fits are correlated:
      - the parameters should be 'some' smooth function of the additional observable.
      - the probability of the fits should be 'some' smooth function of the additional observable.
      - the sum of all signals should match the integral of the total signal. 
     
  now the question:
     how can i simultaniously fit the ten histos? is there a ROOT-class?
     are there some examples? one could think of some 
     multi-constraint, iterative fitting method; or one could try to
     fit the surface of a TH2F filled with 
        h->Fill(missingmass, angle, totalcountsofthisbin).   
     i'm currently working on this problem, but the output is not yet what i'm aiming for. 
 
thanx in advance,
  martin



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