ROOT 6.08/07 Reference Guide |
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):
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 46 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::Fitter * | GetFitter () |
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... | |
virtual const char * | ClassName () const |
Returns name of class to which the object belongs. More... | |
virtual void | Clear (Option_t *="") |
virtual TObject * | Clone (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 TObject * | DrawClone (Option_t *option="") const |
Draw a clone of this object in the current pad. 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 TObject * | FindObject (const char *name) const |
Must be redefined in derived classes. More... | |
virtual TObject * | FindObject (const TObject *obj) const |
Must be redefined in derived classes. More... | |
virtual Option_t * | GetDrawOption () 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_t * | GetOption () 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... | |
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... | |
Bool_t | IsOnHeap () const |
virtual Bool_t | IsSortable () const |
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... | |
void * | operator new (size_t sz) |
void * | operator new (size_t sz, void *vp) |
void * | operator new[] (size_t sz) |
void * | operator new[] (size_t sz, void *vp) |
TObject & | operator= (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... | |
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 |
TH1 * | fDenominator |
Double_t | fEpsilon |
Bool_t | fFitDone |
ROOT::Fit::Fitter * | fFitter |
TF1 * | fFunction |
TH1 * | fNumerator |
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, kBitMask = 0x00ffffff } |
enum | { kSingleKey = BIT(0), kOverwrite = BIT(1), kWriteDelete = BIT(2) } |
enum | EStatusBits { kCanDelete = BIT(0), kMustCleanup = BIT(3), kObjInCanvas = 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>
TBinomialEfficiencyFitter::TBinomialEfficiencyFitter | ( | ) |
default constructor
Definition at line 101 of file TBinomialEfficiencyFitter.cxx.
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 121 of file TBinomialEfficiencyFitter.cxx.
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destructor
Definition at line 131 of file TBinomialEfficiencyFitter.cxx.
Compute the likelihood.
Definition at line 320 of file TBinomialEfficiencyFitter.cxx.
Definition at line 71 of file TBinomialEfficiencyFitter.h.
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 195 of file TBinomialEfficiencyFitter.cxx.
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 162 of file TBinomialEfficiencyFitter.cxx.
Initialize with a new set of inputs.
Definition at line 139 of file TBinomialEfficiencyFitter.cxx.
Set the required integration precision, see TF1::Integral()
Definition at line 152 of file TBinomialEfficiencyFitter.cxx.
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Definition at line 54 of file TBinomialEfficiencyFitter.h.
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Definition at line 49 of file TBinomialEfficiencyFitter.h.
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Definition at line 52 of file TBinomialEfficiencyFitter.h.
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Definition at line 53 of file TBinomialEfficiencyFitter.h.
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Definition at line 56 of file TBinomialEfficiencyFitter.h.
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Definition at line 51 of file TBinomialEfficiencyFitter.h.
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Definition at line 50 of file TBinomialEfficiencyFitter.h.
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Definition at line 55 of file TBinomialEfficiencyFitter.h.