Re: [ROOT] multidimensional/multicorrolated/multiconstrained fit

From: Edmond Offermann (edmondoffermann@yahoo.com)
Date: Sun Nov 07 2004 - 16:38:43 MET

```Hi Rene and Martin,

I think you want the TH1's stored in a TH2 where the the TH1's are a
function
of the missing mass and the additional dimension of a TH2 is used for
the
angle .
To me it is not clear when using the THStack where the angle info is
stored .
But besides that detail, the real "meat" is in how to specify the fit
function and
the objective function (something like H1FitChisquare and
H1FitLikelihood) .

The descripton/wishlist of Martin is from a statistical point not clear
. The only
part of the description I understand is that he wants to fit 10 histos
simultaneously and that the fit parameters should vary smoothly as a
function
of the angle :

suppose for the 1-dim case your fitting function was :

z_fit = b0 + b1 x +b2 x^2 + a0 exp(-a1 (x-a2)^2) where x is the missing
mass
b0,b1 and b2 the background  par and a0,a1 and a2 the parameters for a
Gauss

now for the 2-dim case :

z_fit = b0 + b1 x + b2 x^2 +b3 y + b4 y^2 + b5 xy + a0 exp(-a1
(x-a2)^2)

where a0 = d0 + d1 y , a1 = e0 + e1 y , ......  if you assume a linear
angle dependence

The way you code this up is by using directly minuit as showm in
tutorials/Ifit.C

Eddy

--- Rene Brun <brun@pcbrun.cern.ch> wrote:

> Hi Martin,
>
> A possible solution could be via THStack and implement THStack::Fit.
> A THStack is a list of histograms.
> The existing fitting algorithms (H1FitChisquare and H1FitLikelihood)
> could be extended to support a THStack.
>
> If somebody has a better idea, let me know.
>
> Rene Brun
>
> On
> Sat, 6 Nov 2004, schulte-wissermann wrote:
>
> > 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
> >       - 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.
> >