library: libHist #include "TFractionFitter.h" |
TFractionFitter
class description - source file - inheritance tree (.pdf)
private:
void CheckConsistency()
void CheckParNo(Int_t parm) const
void ComputeChisquareLambda()
void ComputeFCN(Int_t& npar, Double_t* gin, Double_t& f, Double_t* par, Int_t flag)
void FindPrediction(int bin, double* fractions, double& Ti, int& k0, double& Aki) const
void GetRanges(Int_t& minX, Int_t& maxX, Int_t& minY, Int_t& maxY, Int_t& minZ, Int_t& maxZ) const
public:
TFractionFitter()
TFractionFitter(TH1* data, TObjArray* MCs)
virtual ~TFractionFitter()
static TClass* Class()
void Constrain(Int_t parm, Double_t low, Double_t high)
void ErrorAnalysis(Double_t UP)
Int_t Fit()
Double_t GetChisquare() const
TVirtualFitter* GetFitter() const
TH1* GetMCPrediction(Int_t parm) const
Int_t GetNDF() const
TH1* GetPlot()
Double_t GetProb() const
void GetResult(Int_t parm, Double_t& value, Double_t& error) const
virtual TClass* IsA() const
void ReleaseRangeX()
void ReleaseRangeY()
void ReleaseRangeZ()
void SetData(TH1* data)
void SetMC(Int_t parm, TH1* MC)
void SetRangeX(Int_t low, Int_t high)
void SetRangeY(Int_t low, Int_t high)
void SetRangeZ(Int_t low, Int_t high)
void SetWeight(Int_t parm, TH1* weight)
virtual void ShowMembers(TMemberInspector& insp, char* parent)
virtual void Streamer(TBuffer& b)
void StreamerNVirtual(TBuffer& b)
void UnConstrain(Int_t parm)
protected:
Bool_t fFitDone flags whether a valid fit has been performed
Int_t fLowLimitX first bin in X dimension
Int_t fHighLimitX last bin in X dimension
Int_t fLowLimitY first bin in Y dimension
Int_t fHighLimitY last bin in Y dimension
Int_t fLowLimitZ first bin in Z dimension
Int_t fHighLimitZ last bin in Z dimension
Int_t fNpfits Number of points used in the fit
Int_t fNDF Number of degrees of freedom in the fit
Double_t fChisquare Template fit chisquare
TObjArray fAji array of pointers to predictions of real template distributions
TH1* fData pointer to the "data" histogram to be fitted to
TObjArray fMCs array of pointers to template histograms
TObjArray fWeights array of pointers to corresponding weight factors (may be null)
Double_t fIntegralData "data" histogram content integral over allowed fit range
Double_t* fIntegralMCs same for template histograms (weights not taken into account)
Double_t* fFractions template fractions scaled to the "data" histogram statistics
TH1* fPlot pointer to histogram containing summed template predictions
Int_t fNpar number of fit parameters
Fits MC fractions to data histogram (a la HMCMLL, see R. Barlow and C. Beeston,
Comp. Phys. Comm. 77 (1993) 219-228, and http://www.hep.man.ac.uk/~roger/hfrac.f).
The virtue of this fit is that it takes into account both data and Monte Carlo
statistical uncertainties. The way in which this is done is through a standard
likelihood fit using Poisson statistics; however, the template (MC) predictions
are also varied within statistics, leading to additional contributions to the
overall likelihood. This leads to many more fit parameters (one per bin per
template), but the minimisation with respect to these additional parameters is
done analytically rather than introducing them as formal fit parameters. Some
special care needs to be taken in the case of bins with zero content. For more
details please see the original publication cited above.
An example application of this fit is given below. For a TH1* histogram
("data") fitted as the sum of three Monte Carlo sources ("mc"):
{
TH1F *data; //data histogram
TH1F *mc0; // first MC histogram
TH1F *mc1; // second MC histogram
TH1F *mc2; // third MC histogram
.... // retrieve histograms
TObjArray *mc = new TObjArray(3); // MC histograms are put in this array
mc->Add(mc0);
mc->Add(mc1);
mc->Add(mc2);
TFractionFitter* fit = new TFractionFitter(data, mc); // initialise
fit->Constrain(1,0.0,1.0); // constrain fraction 1 to be between 0 and 1
fit->SetRangeX(1,15); // use only the first 15 bins in the fit
Int_t status = fit->Fit(); // perform the fit
cout << "fit status: " << status << endl;
if (status == 0) { // check on fit status
TH1F* prediction = (TH1F*) fit->GetPlot();
data->Draw("Ep");
result->Draw("same");
}
}
Instantiation
=============
A fit object is instantiated through
TFractionFitter* fit = new TFractionFitter(data, mc);
A number of basic checks (intended to ensure that the template histograms
represent the same "kind" of distribution as the data one) are carried out.
The TVirtualFitter object is then addressed and all fit parameters (the
template fractions) declared (initially unbounded).
Applying constraints
====================
Fit parameters can be constrained through
fit->Constrain(parameter #, lower bound, upper bound);
Setting lower bound = upper bound = 0 removes the constraint (a la Minuit);
however, a function
fit->Unconstrain(parameter #)
is also provided to simplify this.
Setting parameter values
========================
The function
TVirtualFitter* vFit = fit->GetFitter();
is provided for direct access to the TVirtualFitter object. This allows to
set and fix parameter values, and set step sizes directly.
Restricting the fit range
=========================
The fit range can be restricted through
fit->SetRangeX(first bin #, last bin #);
and freed using
fit->ReleaseRangeX();
For 2D histograms the Y range can be similarly restricted using
fit->SetRangeY(first bin #, last bin #);
fit->ReleaseRangeY();
and for 3D histograms also
fit->SetRangeZ(first bin #, last bin #);
fit->ReleaseRangeZ();
Weights histograms
==================
Weights histograms (for a motivation see the above publication) can be specified
for the individual MC sources through
fit->SetWeight(parameter #, pointer to weights histogram);
and unset by specifying a null pointer.
Obtaining fit results
=====================
The fit is carried out through
Int_t status = fit->Fit();
where status is the code returned from the "MINIMIZE" command. For fits
that converged, parameter values and errors can be obtained through
fit->GetResult(parameter #, value, error);
and the histogram corresponding to the total Monte Carlo prediction (which
is not the same as a simple weighted sum of the input Monte Carlo distributions)
can be obtained by
TH1* result = fit->GetPlot();
Using different histograms
==========================
It is possible to change the histogram being fitted through
fit->SetData(TH1* data);
and to change the template histogram for a given parameter number through
fit->SetMC(parameter #, TH1* MC);
This can speed up code in case of multiple data or template histograms;
however, it should be done with care as any settings are taken over from
the previous fit. In addition, neither the dimensionality nor the numbers of
bins of the histograms should change (in that case it is better to instantiate
a new TFractionFitter object).
Errors
======
Any serious inconsistency results in an error.
TFractionFitter() :
fFitDone(kFALSE),fData(0), fPlot(0)
TFractionFitter default constructor.
TFractionFitter(TH1* data, TObjArray *MCs) :
fFitDone(kFALSE), fChisquare(0), fPlot(0)
TFractionFitter constructor. Does a complete initialisation (including
consistency checks, default fit range as the whole histogram but without
under- and overflows, and declaration of the fit parameters). Note that
the histograms are not copied, only references are used.
Arguments:
data: histogram to be fitted
MCs: array of TH1* corresponding template distributions
~TFractionFitter()
TFractionFitter default destructor
void SetData(TH1* data)
Change the histogram to be fitted to. Notes:
- Parameter constraints and settings are retained from a possible previous fit.
- Modifying the dimension or number of bins results in an error (in this case
rather instantiate a new TFractionFitter object)
void SetMC(Int_t parm, TH1* MC)
Change the histogram for template number <parm>. Notes:
- Parameter constraints and settings are retained from a possible previous fit.
- Modifying the dimension or number of bins results in an error (in this case
rather instantiate a new TFractionFitter object)
void SetWeight(Int_t parm, TH1* weight)
Set bin by bin weights for template number <parm> (the parameter numbering
follows that of the input template vector).
Weights can be "unset" by passing a null pointer.
Consistency of the weights histogram with the data histogram is checked at
this point, and an error in case of problems.
TVirtualFitter* GetFitter() const
Give direct access to the underlying minimisation class. This can be
used e.g. to modify parameter values or step sizes.
void CheckParNo(Int_t parm) const
Function for internal use, checking parameter validity
An invalid parameter results in an error.
void SetRangeX(Int_t low, Int_t high)
Set the X range of the histogram to be used in the fit.
Use ReleaseRangeX() to go back to fitting the full histogram.
The consistency check ensures that no empty fit range occurs (and also
recomputes the bin content integrals).
Arguments:
low: lower X bin number
high: upper X bin number
void ReleaseRangeX()
Release restrictions on the X range of the histogram to be used in the fit.
void SetRangeY(Int_t low, Int_t high)
Set the Y range of the histogram to be used in the fit (2D or 3D histograms only).
Use ReleaseRangeY() to go back to fitting the full histogram.
The consistency check ensures that no empty fit range occurs (and also
recomputes the bin content integrals).
Arguments:
low: lower Y bin number
high: upper Y bin number
void ReleaseRangeY()
Release restrictions on the Y range of the histogram to be used in the fit.
void SetRangeZ(Int_t low, Int_t high)
Set the Z range of the histogram to be used in the fit (3D histograms only).
Use ReleaseRangeY() to go back to fitting the full histogram.
The consistency check ensures that no empty fit range occurs (and also
recomputes the bin content integrals).
Arguments:
low: lower Y bin number
high: upper Y bin number
void ReleaseRangeZ()
Release restrictions on the Z range of the histogram to be used in the fit.
void Constrain(Int_t parm, Double_t low, Double_t high)
Constrain the values of parameter number <parm> (the parameter numbering
follows that of the input template vector).
Use UnConstrain() to remove this constraint.
void UnConstrain(Int_t parm)
Remove the constraints on the possible values of parameter <parm>.
void CheckConsistency()
Function used internally to check the consistency between the
various histograms. Checks are performed on nonexistent or empty
histograms, the precise histogram class, and the number of bins.
In addition, integrals over the "allowed" bin ranges are computed.
Any inconsistency results in a error.
Int_t Fit()
Perform the fit with the default UP value.
The value returned is the minimisation status.
void ErrorAnalysis(Double_t UP)
Set UP to the given value (see class TMinuit), and perform a MINOS minimisation.
void GetResult(Int_t parm, Double_t& value, Double_t& error) const
Obtain the fit result for parameter <parm> (the parameter numbering
follows that of the input template vector).
TH1* GetPlot()
Return the "template prediction" corresponding to the fit result (this is not
the same as the weighted sum of template distributions, as template statistical
uncertainties are taken into account).
Note that the name of this histogram will simply be the same as that of the
"data" histogram, prefixed with the string "Fraction fit to hist: ".
void GetRanges(Int_t& minX, Int_t& maxX, Int_t& minY, Int_t& maxY,
Int_t& minZ, Int_t& maxZ) const
Used internally to obtain the bin ranges according to the dimensionality of
the histogram and the limits set by hand.
void ComputeFCN(Int_t& /*npar*/, Double_t* /*gin*/,
Double_t& f, Double_t* xx, Int_t flag)
Used internally to compute the likelihood value.
void FindPrediction(int bin, Double_t *fractions, Double_t &Ti, int& k0, Double_t &Aki) const
Function used internally to obtain the template prediction in the individual bins
Double_t GetChisquare() const
Return the likelihood ratio Chi-squared (chi2) for the fit.
The value is computed when the fit is executed successfully.
Chi2 calculation is based on the "likelihood ratio" lambda,
lambda = L(y;n) / L(m;n),
where L(y;n) is the likelihood of the fit result <y> describing the data <n>
and L(m;n) is the likelihood of an unknown "true" underlying distribution
<m> describing the data <n>. Since <m> is unknown, the data distribution is
used instead,
lambda = L(y;n) / L(n;n).
Note that this ratio is 1 if the fit is perfect. The chi2 value is then
computed according to
chi2 = -2*ln(lambda).
This parameter can be shown to follow a Chi-square distribution. See for
example S. Baker and R. Cousins, "Clarification of the use of chi-square
and likelihood functions in fits to histograms", Nucl. Instr. Meth. A221,
pp. 437-442 (1984)
Int_t GetNDF() const
return the number of degrees of freedom in the fit
the fNDF parameter has been previously computed during a fit.
The number of degrees of freedom corresponds to the number of points
used in the fit minus the number of templates.
Double_t GetProb() const
return the fit probability
void ComputeChisquareLambda()
Method used internally to compute the likelihood ratio chi2
See the function GetChisquare() for details
TH1* GetMCPrediction(Int_t parm) const
Return the adjusted MC template (Aji) for template (parm).
Note that the (Aji) times fractions only sum to the total prediction
of the fit if all weights are 1.
Inline Functions
TClass* Class()
TClass* IsA() const
void ShowMembers(TMemberInspector& insp, char* parent)
void Streamer(TBuffer& b)
void StreamerNVirtual(TBuffer& b)
Author: Frank Filthaut filthaut@hef.kun.nl 20/05/2002
Last update: root/hist:$Name: $:$Id: TFractionFitter.cxx,v 1.10 2004/08/18 12:29:44 brun Exp $
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