Logo ROOT   6.19/01
Reference Guide
TBinomialEfficiencyFitter Class Reference

Binomial fitter for the division of two histograms.

Use when you need 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, and when you have a parametrization available for the efficiency as a function of the variable(s) under consideration.

A very common problem when estimating efficiencies is that of error estimation: when no other information is available than the total number of events N and the selected number n, the best estimate for the selection efficiency p is n/N. Standard binomial statistics dictates that the uncertainty (this presupposes sufficiently high statistics that an approximation by a normal distribution is reasonable) on p, given N, is

\[ \sqrt{\frac{p(1-p)}{N}} \]

However, when p is estimated as n/N, fluctuations from the true p to its estimate become important, especially for low numbers of events, and giving rise to biased results.

When fitting a parametrized efficiency, these problems can largely be overcome, as a hypothesized true efficiency is available by construction. Even so, simply using the corresponding uncertainty still presupposes that Gaussian errors yields a reasonable approximation. When using, instead of binned efficiency histograms, the original numerator and denominator histograms, a binned maximum likelihood can be constructed as the product of bin-by-bin binomial probabilities to select n out of N events. Assuming that a correct parametrization of the efficiency is provided, this construction in general yields less biased results (and is much less sensitive to binning details).

A generic use of this method is given below (note that the method works for 2D and 3D histograms as well):

{
TH1* denominator; // denominator histogram
TH1* numerator; // corresponding numerator histogram
TF1* eff; // efficiency parametrization
.... // set step sizes and initial parameter
.... // values for the fit function
.... // possibly also set ranges, see TF1::SetRange()
numerator, denominator);
Int_t status = f->Fit(eff, "I");
if (status == 0) {
// if the fit was successful, display bin-by-bin efficiencies
// as well as the result of the fit
numerator->Sumw2();
TH1* hEff = dynamic_cast<TH1*>(numerator->Clone("heff"));
hEff->Divide(hEff, denominator, 1.0, 1.0, "B");
hEff->Draw("E");
eff->Draw("same");
}
}

Note that this method cannot be expected to yield reliable results when using weighted histograms (because the likelihood computation will be incorrect).

Definition at line 42 of file TBinomialEfficiencyFitter.h.

Public Member Functions

 TBinomialEfficiencyFitter ()
 default constructor More...
 
 TBinomialEfficiencyFitter (const TH1 *numerator, const TH1 *denominator)
 Constructor. More...
 
virtual ~TBinomialEfficiencyFitter ()
 destructor More...
 
Double_t EvaluateFCN (const Double_t *par)
 
TFitResultPtr Fit (TF1 *f1, Option_t *option="")
 Carry out the fit of the given function to the given histograms. More...
 
ROOT::Fit::FitterGetFitter ()
 Provide access to the underlying fitter object. More...
 
void Set (const TH1 *numerator, const TH1 *denominator)
 Initialize with a new set of inputs. More...
 
void SetPrecision (Double_t epsilon)
 Set the required integration precision, see TF1::Integral() More...
 
- Public Member Functions inherited from TObject
 TObject ()
 TObject constructor. More...
 
 TObject (const TObject &object)
 TObject copy ctor. More...
 
virtual ~TObject ()
 TObject destructor. More...
 
void AbstractMethod (const char *method) const
 Use this method to implement an "abstract" method that you don't want to leave purely abstract. More...
 
virtual void AppendPad (Option_t *option="")
 Append graphics object to current pad. More...
 
virtual void Browse (TBrowser *b)
 Browse object. May be overridden for another default action. More...
 
ULong_t CheckedHash ()
 Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object. More...
 
virtual const char * ClassName () const
 Returns name of class to which the object belongs. More...
 
virtual void Clear (Option_t *="")
 
virtual TObjectClone (const char *newname="") const
 Make a clone of an object using the Streamer facility. More...
 
virtual Int_t Compare (const TObject *obj) const
 Compare abstract method. More...
 
virtual void Copy (TObject &object) const
 Copy this to obj. More...
 
virtual void Delete (Option_t *option="")
 Delete this object. More...
 
virtual Int_t DistancetoPrimitive (Int_t px, Int_t py)
 Computes distance from point (px,py) to the object. More...
 
virtual void Draw (Option_t *option="")
 Default Draw method for all objects. More...
 
virtual void DrawClass () const
 Draw class inheritance tree of the class to which this object belongs. More...
 
virtual TObjectDrawClone (Option_t *option="") const
 Draw a clone of this object in the current selected pad for instance with: gROOT->SetSelectedPad(gPad). More...
 
virtual void Dump () const
 Dump contents of object on stdout. More...
 
virtual void Error (const char *method, const char *msgfmt,...) const
 Issue error message. More...
 
virtual void Execute (const char *method, const char *params, Int_t *error=0)
 Execute method on this object with the given parameter string, e.g. More...
 
virtual void Execute (TMethod *method, TObjArray *params, Int_t *error=0)
 Execute method on this object with parameters stored in the TObjArray. More...
 
virtual void ExecuteEvent (Int_t event, Int_t px, Int_t py)
 Execute action corresponding to an event at (px,py). More...
 
virtual void Fatal (const char *method, const char *msgfmt,...) const
 Issue fatal error message. More...
 
virtual TObjectFindObject (const char *name) const
 Must be redefined in derived classes. More...
 
virtual TObjectFindObject (const TObject *obj) const
 Must be redefined in derived classes. More...
 
virtual Option_tGetDrawOption () const
 Get option used by the graphics system to draw this object. More...
 
virtual const char * GetIconName () const
 Returns mime type name of object. More...
 
virtual const char * GetName () const
 Returns name of object. More...
 
virtual char * GetObjectInfo (Int_t px, Int_t py) const
 Returns string containing info about the object at position (px,py). More...
 
virtual Option_tGetOption () const
 
virtual const char * GetTitle () const
 Returns title of object. More...
 
virtual UInt_t GetUniqueID () const
 Return the unique object id. More...
 
virtual Bool_t HandleTimer (TTimer *timer)
 Execute action in response of a timer timing out. More...
 
virtual ULong_t Hash () const
 Return hash value for this object. More...
 
Bool_t HasInconsistentHash () const
 Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e. More...
 
virtual void Info (const char *method, const char *msgfmt,...) const
 Issue info message. More...
 
virtual Bool_t InheritsFrom (const char *classname) const
 Returns kTRUE if object inherits from class "classname". More...
 
virtual Bool_t InheritsFrom (const TClass *cl) const
 Returns kTRUE if object inherits from TClass cl. More...
 
virtual void Inspect () const
 Dump contents of this object in a graphics canvas. More...
 
void InvertBit (UInt_t f)
 
virtual Bool_t IsEqual (const TObject *obj) const
 Default equal comparison (objects are equal if they have the same address in memory). More...
 
virtual Bool_t IsFolder () const
 Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More...
 
R__ALWAYS_INLINE Bool_t IsOnHeap () const
 
virtual Bool_t IsSortable () const
 
R__ALWAYS_INLINE Bool_t IsZombie () const
 
virtual void ls (Option_t *option="") const
 The ls function lists the contents of a class on stdout. More...
 
void MayNotUse (const char *method) const
 Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary). More...
 
virtual Bool_t Notify ()
 This method must be overridden to handle object notification. More...
 
void Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const
 Use this method to declare a method obsolete. More...
 
void operator delete (void *ptr)
 Operator delete. More...
 
void operator delete[] (void *ptr)
 Operator delete []. More...
 
voidoperator new (size_t sz)
 
voidoperator new (size_t sz, void *vp)
 
voidoperator new[] (size_t sz)
 
voidoperator new[] (size_t sz, void *vp)
 
TObjectoperator= (const TObject &rhs)
 TObject assignment operator. More...
 
virtual void Paint (Option_t *option="")
 This method must be overridden if a class wants to paint itself. More...
 
virtual void Pop ()
 Pop on object drawn in a pad to the top of the display list. More...
 
virtual void Print (Option_t *option="") const
 This method must be overridden when a class wants to print itself. More...
 
virtual Int_t Read (const char *name)
 Read contents of object with specified name from the current directory. More...
 
virtual void RecursiveRemove (TObject *obj)
 Recursively remove this object from a list. More...
 
void ResetBit (UInt_t f)
 
virtual void SaveAs (const char *filename="", Option_t *option="") const
 Save this object in the file specified by filename. More...
 
virtual void SavePrimitive (std::ostream &out, Option_t *option="")
 Save a primitive as a C++ statement(s) on output stream "out". More...
 
void SetBit (UInt_t f, Bool_t set)
 Set or unset the user status bits as specified in f. More...
 
void SetBit (UInt_t f)
 
virtual void SetDrawOption (Option_t *option="")
 Set drawing option for object. More...
 
virtual void SetUniqueID (UInt_t uid)
 Set the unique object id. More...
 
virtual void SysError (const char *method, const char *msgfmt,...) const
 Issue system error message. More...
 
R__ALWAYS_INLINE Bool_t TestBit (UInt_t f) const
 
Int_t TestBits (UInt_t f) const
 
virtual void UseCurrentStyle ()
 Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. More...
 
virtual void Warning (const char *method, const char *msgfmt,...) const
 Issue warning message. More...
 
virtual Int_t Write (const char *name=0, Int_t option=0, Int_t bufsize=0)
 Write this object to the current directory. More...
 
virtual Int_t Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
 Write this object to the current directory. More...
 

Protected Attributes

Bool_t fAverage
 
TH1fDenominator
 
Double_t fEpsilon
 
Bool_t fFitDone
 
ROOT::Fit::FitterfFitter
 
TF1fFunction
 
TH1fNumerator
 
Bool_t fRange
 

Private Member Functions

void ComputeFCN (Double_t &f, const Double_t *par)
 Compute the likelihood. More...
 

Additional Inherited Members

- Public Types inherited from TObject
enum  {
  kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kInconsistent = 0x08000000,
  kBitMask = 0x00ffffff
}
 
enum  { kSingleKey = BIT(0), kOverwrite = BIT(1), kWriteDelete = BIT(2) }
 
enum  EDeprecatedStatusBits { kObjInCanvas = BIT(3) }
 
enum  EStatusBits {
  kCanDelete = BIT(0), kMustCleanup = BIT(3), kIsReferenced = BIT(4), kHasUUID = BIT(5),
  kCannotPick = BIT(6), kNoContextMenu = BIT(8), kInvalidObject = BIT(13)
}
 
- Static Public Member Functions inherited from TObject
static Long_t GetDtorOnly ()
 Return destructor only flag. More...
 
static Bool_t GetObjectStat ()
 Get status of object stat flag. More...
 
static void SetDtorOnly (void *obj)
 Set destructor only flag. More...
 
static void SetObjectStat (Bool_t stat)
 Turn on/off tracking of objects in the TObjectTable. More...
 
- Protected Member Functions inherited from TObject
virtual void DoError (int level, const char *location, const char *fmt, va_list va) const
 Interface to ErrorHandler (protected). More...
 
void MakeZombie ()
 

#include <TBinomialEfficiencyFitter.h>

Inheritance diagram for TBinomialEfficiencyFitter:
[legend]

Constructor & Destructor Documentation

◆ TBinomialEfficiencyFitter() [1/2]

TBinomialEfficiencyFitter::TBinomialEfficiencyFitter ( )

default constructor

Definition at line 102 of file TBinomialEfficiencyFitter.cxx.

◆ TBinomialEfficiencyFitter() [2/2]

TBinomialEfficiencyFitter::TBinomialEfficiencyFitter ( const TH1 numerator,
const TH1 denominator 
)

Constructor.

Note that no objects are copied, so it is up to the user to ensure that the histogram pointers remain valid.

Both histograms need to be "consistent". This is not checked here, but in TBinomialEfficiencyFitter::Fit().

Definition at line 122 of file TBinomialEfficiencyFitter.cxx.

◆ ~TBinomialEfficiencyFitter()

TBinomialEfficiencyFitter::~TBinomialEfficiencyFitter ( )
virtual

destructor

Definition at line 132 of file TBinomialEfficiencyFitter.cxx.

Member Function Documentation

◆ ComputeFCN()

void TBinomialEfficiencyFitter::ComputeFCN ( Double_t f,
const Double_t par 
)
private

Compute the likelihood.

Definition at line 325 of file TBinomialEfficiencyFitter.cxx.

◆ EvaluateFCN()

Double_t TBinomialEfficiencyFitter::EvaluateFCN ( const Double_t par)
inline

Definition at line 67 of file TBinomialEfficiencyFitter.h.

◆ Fit()

TFitResultPtr TBinomialEfficiencyFitter::Fit ( TF1 f1,
Option_t option = "" 
)

Carry out the fit of the given function to the given histograms.

If option "I" is used, the fit function will be averaged over the bin (the default is to evaluate it simply at the bin center).

If option "R" is used, the fit range will be taken from the fit function (the default is to use the entire histogram).

If option "S" a TFitResult object is returned and it can be used to obtain additional fit information, like covariance or correlation matrix.

Note that all parameter values, limits, and step sizes are copied from the input fit function f1 (so they should be set before calling this method. This is particularly relevant for the step sizes, taken to be the "error" set on input, as a null step size usually fixes the corresponding parameter. That is protected against, but in such cases an arbitrary starting step size will be used, and the reliability of the fit should be questioned). If parameters are to be fixed, this should be done by specifying non-null parameter limits, with lower limits larger than upper limits.

On output, f1 contains the fitted parameters and errors, as well as the number of degrees of freedom, and the goodness-of-fit estimator as given by S. Baker and R. Cousins, Nucl. Instr. Meth. A221 (1984) 437.

Definition at line 196 of file TBinomialEfficiencyFitter.cxx.

◆ GetFitter()

ROOT::Fit::Fitter * TBinomialEfficiencyFitter::GetFitter ( )

Provide access to the underlying fitter object.

This may be useful e.g. for the retrieval of additional information (such as the output covariance matrix of the fit).

Definition at line 163 of file TBinomialEfficiencyFitter.cxx.

◆ Set()

void TBinomialEfficiencyFitter::Set ( const TH1 numerator,
const TH1 denominator 
)

Initialize with a new set of inputs.

Definition at line 140 of file TBinomialEfficiencyFitter.cxx.

◆ SetPrecision()

void TBinomialEfficiencyFitter::SetPrecision ( Double_t  epsilon)

Set the required integration precision, see TF1::Integral()

Definition at line 153 of file TBinomialEfficiencyFitter.cxx.

Member Data Documentation

◆ fAverage

Bool_t TBinomialEfficiencyFitter::fAverage
protected

Definition at line 50 of file TBinomialEfficiencyFitter.h.

◆ fDenominator

TH1* TBinomialEfficiencyFitter::fDenominator
protected

Definition at line 45 of file TBinomialEfficiencyFitter.h.

◆ fEpsilon

Double_t TBinomialEfficiencyFitter::fEpsilon
protected

Definition at line 48 of file TBinomialEfficiencyFitter.h.

◆ fFitDone

Bool_t TBinomialEfficiencyFitter::fFitDone
protected

Definition at line 49 of file TBinomialEfficiencyFitter.h.

◆ fFitter

ROOT::Fit::Fitter* TBinomialEfficiencyFitter::fFitter
protected

Definition at line 52 of file TBinomialEfficiencyFitter.h.

◆ fFunction

TF1* TBinomialEfficiencyFitter::fFunction
protected

Definition at line 47 of file TBinomialEfficiencyFitter.h.

◆ fNumerator

TH1* TBinomialEfficiencyFitter::fNumerator
protected

Definition at line 46 of file TBinomialEfficiencyFitter.h.

◆ fRange

Bool_t TBinomialEfficiencyFitter::fRange
protected

Definition at line 51 of file TBinomialEfficiencyFitter.h.

Libraries for TBinomialEfficiencyFitter:
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The documentation for this class was generated from the following files: