 ROOT   Reference Guide TRolke Class Reference

This class computes confidence intervals for the rate of a Poisson process in the presence of uncertain background and/or efficiency.

The treatment and the resulting limits are fully frequentist. The limit calculations make use of the profile likelihood method.

For a full list of methods and their syntax, and build instructions, consult the header file TRolke.h.

Examples/tutorials are found in the separate file Rolke.C

### TRolke implements the following Models

The signal is always assumed to be Poisson, with the following combinations of models of background and detection efficiency:

If unsure, first consider model 3, 4 or 5.

1: SetPoissonBkgBinomEff(x,y,z,tau,m)

Background: Poisson

when the background is simultaneously measured from sidebands (or MC), and the signal efficiency was determined from Monte Carlo

2: SetPoissonBkgGaussEff(x,y,em,sde,tau)

Background: Poisson

when the background is simultaneously measured from sidebands (or MC), and the efficiency is modeled as Gaussian

3: SetGaussBkgGaussEff(x,bm,em,sde,sdb)

Background: Gaussian

when background and efficiency can both be modeled as Gaussian.

4: SetPoissonBkgKnownEff(x,y,tau,e)

Background: Poisson
Efficiency: Known

when the background is simultaneously measured from sidebands (or MC).

5: SetGaussBkgKnownEff(x,bm,sdb,e)

Background: Gaussian
Efficiency: Known

when background is Gaussian

6: SetKnownBkgBinomEff(x,z,b,m)

Background: Known

when signal efficiency was determined from Monte Carlo

7: SetKnownBkgGaussEff(x,em,sde,b)

Background: Known

when background is known and efficiency Gaussian

### Parameters and further explanation

#### For all models:

x = number of observed events in the experiment

Efficiency (e or em) is the detection probability for signal. A low efficiency hence generally means weaker limits. If the efficiency of an experiment (with analysis cuts) is dealt with elsewhere, em or e can be set to one.

#### For Poisson background measurements (sideband or MC):

y = number of observed events in background region
tau =
Either: the ratio between signal and background region
in case background is observed.
Or: the ratio between observed and simulated live-time
in case background is determined from MC.

#### For Gaussian efficiency or background:

bm = estimate of the background
sdb = corresponding standard deviation
em = estimate of the efficiency
sde = corresponding standard deviation

If the efficiency scale of dealt with elsewhere, set em to 1 and sde to the relative uncertainty.

#### For Binomial signal efficiency:

m = number of MC events generated
z = number of MC events observed

#### For the case of known background expectation or known efficiency:

e = true efficiency (considered known)
b = background expectation value (considered known)

The confidence level (CL) is set either at construction time or with either of SetCL or SetCLSigmas

The TRolke method is very similar to the one used in MINUIT (MINOS).

Two options are offered to deal with cases where the maximum likelihood estimate (MLE) is not in the physical region. Version "bounded likelihood" is the one used by MINOS if bounds for the physical region are chosen. Unbounded likelihood (the default) allows the MLE to be in the unphysical region. It has however better coverage. For more details consult the reference (see below).

For a description of the method and its properties:

W.Rolke, A. Lopez, J. Conrad and Fred James "Limits and Confidence Intervals in presence of nuisance parameters" http://lanl.arxiv.org/abs/physics/0403059 Nucl.Instrum.Meth.A551:493-503,2005

#### Should I use TRolke, TFeldmanCousins, TLimit?

1. Does TRolke make TFeldmanCousins obsolete? Certainly not. TFeldmanCousins is the fully frequentist construction and should be used in case of no (or negligible) uncertainties. It is however not capable of treating uncertainties in nuisance parameters. In other words, it does not handle background expectations or signal efficiencies which are known only with some limited accuracy. TRolke is designed for this case and it is shown in the reference above that it has good coverage properties for most cases, and can be used where FeldmannCousins can't.
2. What are the advantages of TRolke over TLimit? TRolke is fully frequentist. TLimit treats nuisance parameters Bayesian. For a coverage study of a Bayesian method refer to physics/0408039 (Tegenfeldt & J.C). However, this note studies the coverage of Feldman&Cousins with Bayesian treatment of nuisance parameters. To make a long story short: using the Bayesian method you might introduce a small amount of over-coverage (though I haven't shown it for TLimit). On the other hand, coverage of course is a not so interesting when you consider yourself a Bayesian.

Definition at line 33 of file TRolke.h.

## Public Member Functions

TRolke (Double_t CL=0.9, Option_t *option="")
Constructor with optional Confidence Level argument. More...

virtual ~TRolke ()
Destructor. More...

Double_t CalculateInterval (Int_t x, Int_t y, Int_t z, Double_t bm, Double_t em, Double_t e, Int_t mid, Double_t sde, Double_t sdb, Double_t tau, Double_t b, Int_t m)
Deprecated and error prone model selection interface. More...

bool GetBounding () const

Double_t GetCL () const

bool GetCriticalNumber (Int_t &ncrit, Int_t maxtry=-1)
get the value of x corresponding to rejection of the null hypothesis. More...

bool GetLimits (Double_t &low, Double_t &high)
Calculate and get the upper and lower limits for the pre-specified model. More...

bool GetLimitsML (Double_t &low, Double_t &high, Int_t &out_x)
get the upper and lower limits for the most likely outcome. More...

bool GetLimitsQuantile (Double_t &low, Double_t &high, Int_t &out_x, Double_t integral=0.5)
get the upper and lower limits for the outcome corresponding to a given quantile. More...

Double_t GetLowerLimit ()
Calculate and get lower limit for the pre-specified model. More...

bool GetSensitivity (Double_t &low, Double_t &high, Double_t pPrecision=0.00001)
get the upper and lower average limits based on the specified model. More...

Double_t GetUpperLimit ()
Calculate and get upper limit for the pre-specified model. More...

void Print (Option_t *) const
Dump internals. Print members. More...

void SetBounding (const bool bnd)

void SetCL (Double_t CL)

void SetCLSigmas (Double_t CLsigmas)

void SetGaussBkgGaussEff (Int_t x, Double_t bm, Double_t em, Double_t sde, Double_t sdb)
Model 3: Background - Gaussian, Efficiency - Gaussian (x,bm,em,sde,sdb) More...

void SetGaussBkgKnownEff (Int_t x, Double_t bm, Double_t sdb, Double_t e)
Model 5: Background - Gaussian, Efficiency - known (x,bm,sdb,e. More...

void SetKnownBkgBinomEff (Int_t x, Int_t z, Int_t m, Double_t b)
Model 6: Background - known, Efficiency - Binomial (x,z,m,b) More...

void SetKnownBkgGaussEff (Int_t x, Double_t em, Double_t sde, Double_t b)
Model 7: Background - known, Efficiency - Gaussian (x,em,sde,b) More...

void SetPoissonBkgBinomEff (Int_t x, Int_t y, Int_t z, Double_t tau, Int_t m)
Model 1: Background - Poisson, Efficiency - Binomial. More...

void SetPoissonBkgGaussEff (Int_t x, Int_t y, Double_t em, Double_t tau, Double_t sde)
Model 2: Background - Poisson, Efficiency - Gaussian. More...

void SetPoissonBkgKnownEff (Int_t x, Int_t y, Double_t tau, Double_t e)
Model 4: Background - Poisson, Efficiency - known (x,y,tau,e) More...

void SetSwitch (bool bnd)
Deprecated name for SetBounding. 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
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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 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)

void SetBit (UInt_t f, Bool_t set)
Set or unset the user status bits as specified in f. More...

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...

## Private Member Functions

Double_t ComputeInterval (Int_t x, Int_t y, Int_t z, Double_t bm, Double_t em, Double_t e, Int_t mid, Double_t sde, Double_t sdb, Double_t tau, Double_t b, Int_t m)
ComputeInterval, the internals. More...

Double_t EvalLikeMod1 (Double_t mu, Int_t x, Int_t y, Int_t z, Double_t tau, Int_t m, Int_t what)
Calculates the Profile Likelihood for MODEL 1: Poisson background/ Binomial Efficiency. More...

Double_t EvalLikeMod2 (Double_t mu, Int_t x, Int_t y, Double_t em, Double_t sde, Double_t tau, Int_t what)
Calculates the Profile Likelihood for MODEL 2: Poisson background/ Gauss Efficiency. More...

Double_t EvalLikeMod3 (Double_t mu, Int_t x, Double_t bm, Double_t em, Double_t sde, Double_t sdb, Int_t what)
Calculates the Profile Likelihood for MODEL 3: Gauss background/ Gauss Efficiency. More...

Double_t EvalLikeMod4 (Double_t mu, Int_t x, Int_t y, Double_t tau, Int_t what)
Calculates the Profile Likelihood for MODEL 4: Poiss background/Efficiency known. More...

Double_t EvalLikeMod5 (Double_t mu, Int_t x, Double_t bm, Double_t sdb, Int_t what)
Calculates the Profile Likelihood for MODEL 5: Gauss background/Efficiency known. More...

Double_t EvalLikeMod6 (Double_t mu, Int_t x, Int_t z, Double_t b, Int_t m, Int_t what)
Calculates the Profile Likelihood for MODEL 6: Background known/Efficiency binomial. More...

Double_t EvalLikeMod7 (Double_t mu, Int_t x, Double_t em, Double_t sde, Double_t b, Int_t what)
Calculates the Profile Likelihood for MODEL 7: background known/Efficiency Gauss. More...

Double_t GetBackground ()
Return a simple background value (estimate/truth) given the pre-specified model. More...

Double_t Interval (Int_t x, Int_t y, Int_t z, Double_t bm, Double_t em, Double_t e, Int_t mid, Double_t sde, Double_t sdb, Double_t tau, Double_t b, Int_t m)
Internal helper function 'Interval'. More...

Double_t LikeGradMod1 (Double_t e, Double_t mu, Int_t x, Int_t y, Int_t z, Double_t tau, Int_t m)
Gradient model likelihood. More...

Double_t Likelihood (Double_t mu, Int_t x, Int_t y, Int_t z, Double_t bm, Double_t em, Int_t mid, Double_t sde, Double_t sdb, Double_t tau, Double_t b, Int_t m, Int_t what)
Internal helper function Chooses between the different profile likelihood functions to use for the different models. More...

Double_t LikeMod1 (Double_t mu, Double_t b, Double_t e, Int_t x, Int_t y, Int_t z, Double_t tau, Int_t m)
Profile Likelihood function for MODEL 1: Poisson background/ Binomial Efficiency. More...

Double_t LikeMod2 (Double_t mu, Double_t b, Double_t e, Int_t x, Int_t y, Double_t em, Double_t tau, Double_t v)
Profile Likelihood function for MODEL 2: Poisson background/Gauss Efficiency. More...

Double_t LikeMod3 (Double_t mu, Double_t b, Double_t e, Int_t x, Double_t bm, Double_t em, Double_t u, Double_t v)
Profile Likelihood function for MODEL 3: Gauss background/Gauss Efficiency. More...

Double_t LikeMod4 (Double_t mu, Double_t b, Int_t x, Int_t y, Double_t tau)
Profile Likelihood function for MODEL 4: Poiss background/Efficiency known. More...

Double_t LikeMod5 (Double_t mu, Double_t b, Int_t x, Double_t bm, Double_t u)
Profile Likelihood function for MODEL 5: Gauss background/Efficiency known. More...

Double_t LikeMod6 (Double_t mu, Double_t b, Double_t e, Int_t x, Int_t z, Int_t m)
Profile Likelihood function for MODEL 6: background known/ Efficiency binomial. More...

Double_t LikeMod7 (Double_t mu, Double_t b, Double_t e, Int_t x, Double_t em, Double_t v)
Profile Likelihood function for MODEL 6: background known/ Efficiency gaussian. More...

Double_t LogFactorial (Int_t n)
LogFactorial function (use the logGamma function via the relation Gamma(n+1) = n! More...

void ProfLikeMod1 (Double_t mu, Double_t &b, Double_t &e, Int_t x, Int_t y, Int_t z, Double_t tau, Int_t m)
Helper for calculation of estimates of efficiency and background for model 1. More...

void SetModelParameters ()

void SetModelParameters (Int_t x, Int_t y, Int_t z, Double_t bm, Double_t em, Double_t e, Int_t mid, Double_t sde, Double_t sdb, Double_t tau, Double_t b, Int_t m)

## Static Private Member Functions

static Double_t EvalMonomial (Double_t x, const Int_t coef[], Int_t N)
Evaluate mononomial. More...

static Double_t EvalPolynomial (Double_t x, const Int_t coef[], Int_t N)
Evaluate polynomial. More...

## Private Attributes

Double_t f_b

Double_t f_bm

Double_t f_e

Double_t f_em

Int_t f_m

Int_t f_mid

Double_t f_sdb

Double_t f_sde

Double_t f_tau

Int_t f_x

Int_t f_y

Int_t f_z

bool fBounding

Double_t fCL

Double_t fLowerLimit

Int_t fNumWarningsDeprecated1

Int_t fNumWarningsDeprecated2

Double_t fUpperLimit

## 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 Types inherited from TObject
enum  { kOnlyPrepStep = BIT(3) } 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 <TRolke.h>

Inheritance diagram for TRolke:
[legend]

## ◆ TRolke()

 TRolke::TRolke ( Double_t CL = 0.9, Option_t * option = "" )

Constructor with optional Confidence Level argument.

'option' is not used.

Definition at line 175 of file TRolke.cxx.

## ◆ ~TRolke()

 TRolke::~TRolke ( )
virtual

Destructor.

Definition at line 189 of file TRolke.cxx.

## ◆ CalculateInterval()

 Double_t TRolke::CalculateInterval ( Int_t x, Int_t y, Int_t z, Double_t bm, Double_t em, Double_t e, Int_t mid, Double_t sde, Double_t sdb, Double_t tau, Double_t b, Int_t m )

Deprecated and error prone model selection interface.

It's use is trongly discouraged. 'mid' is the model ID (1 to 7). This method is provided for backwards compatibility/developer use only. *‍/

• x : number of observed events in the experiment
• y : number of observed events in background region
• z : number of MC events observed
• bm : estimate of the background
• em : estimate of the efficiency
• e : true efficiency (considered known)
• mid : internal model id (really, you should not use this method at all)
• sde : efficiency estimate's standard deviation
• sdb : background estimate's standard deviation
• tau : ratio parameter (read TRolke.cxx for details)
• b : background expectation value (considered known)
• m : number of MC events generated

Definition at line 637 of file TRolke.cxx.

## ◆ ComputeInterval()

 Double_t TRolke::ComputeInterval ( Int_t x, Int_t y, Int_t z, Double_t bm, Double_t em, Double_t e, Int_t mid, Double_t sde, Double_t sdb, Double_t tau, Double_t b, Int_t m )
private

ComputeInterval, the internals.

• x : number of observed events in the experiment
• y : number of observed events in background region
• z : number of MC events observed
• bm : estimate of the background
• em : estimate of the efficiency
• e : true efficiency (considered known)
• mid : internal model id (really, you should not use this method at all)
• sde : efficiency estimate's standard deviation
• sdb : background estimate's standard deviation
• tau : ratio parameter (read TRolke.cxx for details)
• b : background expectation value (considered known)
• m : number of MC events generated

Definition at line 713 of file TRolke.cxx.

## ◆ EvalLikeMod1()

 Double_t TRolke::EvalLikeMod1 ( Double_t mu, Int_t x, Int_t y, Int_t z, Double_t tau, Int_t m, Int_t what )
private

Calculates the Profile Likelihood for MODEL 1: Poisson background/ Binomial Efficiency.

• what = 1: Maximum likelihood estimate is returned
• what = 2: Profile Likelihood of Maximum Likelihood estimate is returned.
• what = 3: Profile Likelihood of Test hypothesis is returned otherwise parameters as described in the beginning of the class)

Definition at line 967 of file TRolke.cxx.

## ◆ EvalLikeMod2()

 Double_t TRolke::EvalLikeMod2 ( Double_t mu, Int_t x, Int_t y, Double_t em, Double_t sde, Double_t tau, Int_t what )
private

Calculates the Profile Likelihood for MODEL 2: Poisson background/ Gauss Efficiency.

• what = 1: Maximum likelihood estimate is returned
• what = 2: Profile Likelihood of Maximum Likelihood estimate is returned.
• what = 3: Profile Likelihood of Test hypothesis is returned otherwise parameters as described in the beginning of the class)

Definition at line 1081 of file TRolke.cxx.

## ◆ EvalLikeMod3()

 Double_t TRolke::EvalLikeMod3 ( Double_t mu, Int_t x, Double_t bm, Double_t em, Double_t sde, Double_t sdb, Int_t what )
private

Calculates the Profile Likelihood for MODEL 3: Gauss background/ Gauss Efficiency.

• what = 1: Maximum likelihood estimate is returned
• what = 2: Profile Likelihood of Maximum Likelihood estimate is returned.
• what = 3: Profile Likelihood of Test hypothesis is returned otherwise parameters as described in the beginning of the class)

Definition at line 1148 of file TRolke.cxx.

## ◆ EvalLikeMod4()

 Double_t TRolke::EvalLikeMod4 ( Double_t mu, Int_t x, Int_t y, Double_t tau, Int_t what )
private

Calculates the Profile Likelihood for MODEL 4: Poiss background/Efficiency known.

• what = 1: Maximum likelihood estimate is returned
• what = 2: Profile Likelihood of Maximum Likelihood estimate is returned.
• what = 3: Profile Likelihood of Test hypothesis is returned otherwise parameters as described in the beginning of the class)

Definition at line 1216 of file TRolke.cxx.

## ◆ EvalLikeMod5()

 Double_t TRolke::EvalLikeMod5 ( Double_t mu, Int_t x, Double_t bm, Double_t sdb, Int_t what )
private

Calculates the Profile Likelihood for MODEL 5: Gauss background/Efficiency known.

• what = 1: Maximum likelihood estimate is returned
• what = 2: Profile Likelihood of Maximum Likelihood estimate is returned.
• what = 3: Profile Likelihood of Test hypothesis is returned otherwise parameters as described in the beginning of the class)

Definition at line 1262 of file TRolke.cxx.

## ◆ EvalLikeMod6()

 Double_t TRolke::EvalLikeMod6 ( Double_t mu, Int_t x, Int_t z, Double_t b, Int_t m, Int_t what )
private

Calculates the Profile Likelihood for MODEL 6: Background known/Efficiency binomial.

• what = 1: Maximum likelihood estimate is returned
• what = 2: Profile Likelihood of Maximum Likelihood estimate is returned.
• what = 3: Profile Likelihood of Test hypothesis is returned otherwise parameters as described in the beginning of the class)

Definition at line 1306 of file TRolke.cxx.

## ◆ EvalLikeMod7()

 Double_t TRolke::EvalLikeMod7 ( Double_t mu, Int_t x, Double_t em, Double_t sde, Double_t b, Int_t what )
private

Calculates the Profile Likelihood for MODEL 7: background known/Efficiency Gauss.

• what = 1: Maximum likelihood estimate is returned
• what = 2: Profile Likelihood of Maximum Likelihood estimate is returned.
• what = 3: Profile Likelihood of Test hypothesis is returned otherwise parameters as described in the beginning of the class)

Definition at line 1365 of file TRolke.cxx.

## ◆ EvalMonomial()

 Double_t TRolke::EvalMonomial ( Double_t x, const Int_t coef[], Int_t N )
staticprivate

Evaluate mononomial.

Definition at line 1429 of file TRolke.cxx.

## ◆ EvalPolynomial()

 Double_t TRolke::EvalPolynomial ( Double_t x, const Int_t coef[], Int_t N )
staticprivate

Evaluate polynomial.

Definition at line 1412 of file TRolke.cxx.

## ◆ GetBackground()

 Double_t TRolke::GetBackground ( )
private

Return a simple background value (estimate/truth) given the pre-specified model.

Definition at line 417 of file TRolke.cxx.

## ◆ GetBounding()

 bool TRolke::GetBounding ( ) const
inline

Definition at line 178 of file TRolke.h.

## ◆ GetCL()

 Double_t TRolke::GetCL ( ) const
inline

Definition at line 121 of file TRolke.h.

## ◆ GetCriticalNumber()

 bool TRolke::GetCriticalNumber ( Int_t & ncrit, Int_t maxtry = -1 )

get the value of x corresponding to rejection of the null hypothesis.

This means a lower limit >0 with the pre-specified Confidence Level. Optionally give maxtry; the maximum value of x to try. Of not, or if maxtry<0 an automatic mode is used.

Definition at line 546 of file TRolke.cxx.

## ◆ GetLimits()

 bool TRolke::GetLimits ( Double_t & low, Double_t & high )

Calculate and get the upper and lower limits for the pre-specified model.

Definition at line 373 of file TRolke.cxx.

## ◆ GetLimitsML()

 bool TRolke::GetLimitsML ( Double_t & low, Double_t & high, Int_t & out_x )

get the upper and lower limits for the most likely outcome.

The returned out_x is the corresponding value of x No uncertainties are considered for the Poisson weights when finding ML.

Definition at line 511 of file TRolke.cxx.

## ◆ GetLimitsQuantile()

 bool TRolke::GetLimitsQuantile ( Double_t & low, Double_t & high, Int_t & out_x, Double_t integral = 0.5 )

get the upper and lower limits for the outcome corresponding to a given quantile.

For integral=0.5 this gives the median limits in repeated experiments. The returned out_x is the corresponding (e.g. median) value of x. No uncertainties are considered for the Poisson weights when calculating the Poisson integral.

Definition at line 481 of file TRolke.cxx.

## ◆ GetLowerLimit()

 Double_t TRolke::GetLowerLimit ( void )

Calculate and get lower limit for the pre-specified model.

Definition at line 407 of file TRolke.cxx.

## ◆ GetSensitivity()

 bool TRolke::GetSensitivity ( Double_t & low, Double_t & high, Double_t pPrecision = 0.00001 )

get the upper and lower average limits based on the specified model.

No uncertainties are considered for the Poisson weights in the averaging sum

Definition at line 446 of file TRolke.cxx.

## ◆ GetUpperLimit()

 Double_t TRolke::GetUpperLimit ( void )

Calculate and get upper limit for the pre-specified model.

Definition at line 397 of file TRolke.cxx.

## ◆ Interval()

 Double_t TRolke::Interval ( Int_t x, Int_t y, Int_t z, Double_t bm, Double_t em, Double_t e, Int_t mid, Double_t sde, Double_t sdb, Double_t tau, Double_t b, Int_t m )
private

Internal helper function 'Interval'.

• x : number of observed events in the experiment
• y : number of observed events in background region
• z : number of MC events observed
• bm : estimate of the background
• em : estimate of the efficiency
• e : true efficiency (considered known)
• mid : internal model id (really, you should not use this method at all)
• sde : efficiency estimate's standard deviation
• sdb : background estimate's standard deviation
• tau : ratio parameter (read TRolke.cxx for details)
• b : background expectation value (considered known)
• m : number of MC events generated

Definition at line 754 of file TRolke.cxx.

## ◆ LikeGradMod1()

 Double_t TRolke::LikeGradMod1 ( Double_t e, Double_t mu, Int_t x, Int_t y, Int_t z, Double_t tau, Int_t m )
private

Gradient model likelihood.

Definition at line 1062 of file TRolke.cxx.

## ◆ Likelihood()

 Double_t TRolke::Likelihood ( Double_t mu, Int_t x, Int_t y, Int_t z, Double_t bm, Double_t em, Int_t mid, Double_t sde, Double_t sdb, Double_t tau, Double_t b, Int_t m, Int_t what )
private

Internal helper function Chooses between the different profile likelihood functions to use for the different models.

Returns evaluation of the profile likelihood functions.

Definition at line 933 of file TRolke.cxx.

## ◆ LikeMod1()

 Double_t TRolke::LikeMod1 ( Double_t mu, Double_t b, Double_t e, Int_t x, Int_t y, Int_t z, Double_t tau, Int_t m )
private

Profile Likelihood function for MODEL 1: Poisson background/ Binomial Efficiency.

Definition at line 1003 of file TRolke.cxx.

## ◆ LikeMod2()

 Double_t TRolke::LikeMod2 ( Double_t mu, Double_t b, Double_t e, Int_t x, Int_t y, Double_t em, Double_t tau, Double_t v )
private

Profile Likelihood function for MODEL 2: Poisson background/Gauss Efficiency.

Definition at line 1126 of file TRolke.cxx.

## ◆ LikeMod3()

 Double_t TRolke::LikeMod3 ( Double_t mu, Double_t b, Double_t e, Int_t x, Double_t bm, Double_t em, Double_t u, Double_t v )
private

Profile Likelihood function for MODEL 3: Gauss background/Gauss Efficiency.

Definition at line 1194 of file TRolke.cxx.

## ◆ LikeMod4()

 Double_t TRolke::LikeMod4 ( Double_t mu, Double_t b, Int_t x, Int_t y, Double_t tau )
private

Profile Likelihood function for MODEL 4: Poiss background/Efficiency known.

Definition at line 1242 of file TRolke.cxx.

## ◆ LikeMod5()

 Double_t TRolke::LikeMod5 ( Double_t mu, Double_t b, Int_t x, Double_t bm, Double_t u )
private

Profile Likelihood function for MODEL 5: Gauss background/Efficiency known.

Definition at line 1287 of file TRolke.cxx.

## ◆ LikeMod6()

 Double_t TRolke::LikeMod6 ( Double_t mu, Double_t b, Double_t e, Int_t x, Int_t z, Int_t m )
private

Profile Likelihood function for MODEL 6: background known/ Efficiency binomial.

Definition at line 1342 of file TRolke.cxx.

## ◆ LikeMod7()

 Double_t TRolke::LikeMod7 ( Double_t mu, Double_t b, Double_t e, Int_t x, Double_t em, Double_t v )
private

Profile Likelihood function for MODEL 6: background known/ Efficiency gaussian.

Definition at line 1397 of file TRolke.cxx.

## ◆ LogFactorial()

 Double_t TRolke::LogFactorial ( Int_t n )
private

LogFactorial function (use the logGamma function via the relation Gamma(n+1) = n!

Definition at line 1448 of file TRolke.cxx.

## ◆ Print()

 void TRolke::Print ( Option_t * ) const
virtual

Dump internals. Print members.

Reimplemented from TObject.

Definition at line 593 of file TRolke.cxx.

## ◆ ProfLikeMod1()

 void TRolke::ProfLikeMod1 ( Double_t mu, Double_t & b, Double_t & e, Int_t x, Int_t y, Int_t z, Double_t tau, Int_t m )
private

Helper for calculation of estimates of efficiency and background for model 1.

Definition at line 1029 of file TRolke.cxx.

## ◆ SetBounding()

 void TRolke::SetBounding ( const bool bnd )
inline

Definition at line 184 of file TRolke.h.

## ◆ SetCL()

 void TRolke::SetCL ( Double_t CL )
inline

Definition at line 124 of file TRolke.h.

## ◆ SetCLSigmas()

 void TRolke::SetCLSigmas ( Double_t CLsigmas )
inline

Definition at line 129 of file TRolke.h.

## ◆ SetGaussBkgGaussEff()

 void TRolke::SetGaussBkgGaussEff ( Int_t x, Double_t bm, Double_t em, Double_t sde, Double_t sdb )

Model 3: Background - Gaussian, Efficiency - Gaussian (x,bm,em,sde,sdb)

• x : number of observed events in the experiment
• bm : estimate of the background
• em : estimate of the efficiency
• sde : efficiency estimate's standard deviation
• sdb : background estimate's standard deviation

Definition at line 252 of file TRolke.cxx.

## ◆ SetGaussBkgKnownEff()

 void TRolke::SetGaussBkgKnownEff ( Int_t x, Double_t bm, Double_t sdb, Double_t e )

Model 5: Background - Gaussian, Efficiency - known (x,bm,sdb,e.

• x : number of observed events in the experiment
• bm : estimate of the background
• sdb : background estimate's standard deviation
• e : true efficiency (considered known)

Definition at line 302 of file TRolke.cxx.

## ◆ SetKnownBkgBinomEff()

 void TRolke::SetKnownBkgBinomEff ( Int_t x, Int_t z, Int_t m, Double_t b )

Model 6: Background - known, Efficiency - Binomial (x,z,m,b)

• x : number of observed events in the experiment
• z : number of MC events observed
• m : number of MC events generated
• b : background expectation value (considered known)

Definition at line 327 of file TRolke.cxx.

## ◆ SetKnownBkgGaussEff()

 void TRolke::SetKnownBkgGaussEff ( Int_t x, Double_t em, Double_t sde, Double_t b )

Model 7: Background - known, Efficiency - Gaussian (x,em,sde,b)

• x : number of observed events in the experiment
• em : estimate of the efficiency
• sde : efficiency estimate's standard deviation
• b : background expectation value (considered known)

Definition at line 352 of file TRolke.cxx.

## ◆ SetModelParameters() [1/2]

 void TRolke::SetModelParameters ( )
private

Definition at line 691 of file TRolke.cxx.

## ◆ SetModelParameters() [2/2]

 void TRolke::SetModelParameters ( Int_t x, Int_t y, Int_t z, Double_t bm, Double_t em, Double_t e, Int_t mid, Double_t sde, Double_t sdb, Double_t tau, Double_t b, Int_t m )
private
• x : number of observed events in the experiment
• y : number of observed events in background region
• z : number of MC events observed
• bm : estimate of the background
• em : estimate of the efficiency
• e : true efficiency (considered known)
• mid : internal model id
• sde : efficiency estimate's standard deviation
• sdb : background estimate's standard deviation
• tau : ratio parameter (read TRolke.cxx for details)
• b : background expectation value (considered known)
• m : number of MC events generated

Definition at line 675 of file TRolke.cxx.

## ◆ SetPoissonBkgBinomEff()

 void TRolke::SetPoissonBkgBinomEff ( Int_t x, Int_t y, Int_t z, Double_t tau, Int_t m )

Model 1: Background - Poisson, Efficiency - Binomial.

• x : number of observed events in the experiment
• y : number of observed events in background region
• z : number of MC events observed
• tau : ratio parameter (read TRolke.cxx for details)
• m : number of MC events generated

Definition at line 201 of file TRolke.cxx.

## ◆ SetPoissonBkgGaussEff()

 void TRolke::SetPoissonBkgGaussEff ( Int_t x, Int_t y, Double_t em, Double_t tau, Double_t sde )

Model 2: Background - Poisson, Efficiency - Gaussian.

• x : number of observed events in the experiment
• y : number of observed events in background region
• em : estimate of the efficiency
• tau : ratio parameter (read TRolke.cxx for details)
• sde : efficiency estimate's standard deviation

Definition at line 226 of file TRolke.cxx.

## ◆ SetPoissonBkgKnownEff()

 void TRolke::SetPoissonBkgKnownEff ( Int_t x, Int_t y, Double_t tau, Double_t e )

Model 4: Background - Poisson, Efficiency - known (x,y,tau,e)

• x : number of observed events in the experiment
• y : number of observed events in background region
• tau : ratio parameter (read TRolke.cxx for details)
• e : true efficiency (considered known)

Definition at line 277 of file TRolke.cxx.

## ◆ SetSwitch()

 void TRolke::SetSwitch ( bool bnd )

Deprecated name for SetBounding.

Definition at line 579 of file TRolke.cxx.

## ◆ f_b

 Double_t TRolke::f_b
private

Definition at line 57 of file TRolke.h.

## ◆ f_bm

 Double_t TRolke::f_bm
private

Definition at line 50 of file TRolke.h.

## ◆ f_e

 Double_t TRolke::f_e
private

Definition at line 52 of file TRolke.h.

## ◆ f_em

 Double_t TRolke::f_em
private

Definition at line 51 of file TRolke.h.

## ◆ f_m

 Int_t TRolke::f_m
private

Definition at line 58 of file TRolke.h.

## ◆ f_mid

 Int_t TRolke::f_mid
private

Definition at line 53 of file TRolke.h.

## ◆ f_sdb

 Double_t TRolke::f_sdb
private

Definition at line 55 of file TRolke.h.

## ◆ f_sde

 Double_t TRolke::f_sde
private

Definition at line 54 of file TRolke.h.

## ◆ f_tau

 Double_t TRolke::f_tau
private

Definition at line 56 of file TRolke.h.

## ◆ f_x

 Int_t TRolke::f_x
private

Definition at line 47 of file TRolke.h.

## ◆ f_y

 Int_t TRolke::f_y
private

Definition at line 48 of file TRolke.h.

## ◆ f_z

 Int_t TRolke::f_z
private

Definition at line 49 of file TRolke.h.

## ◆ fBounding

 bool TRolke::fBounding
private

Definition at line 40 of file TRolke.h.

## ◆ fCL

 Double_t TRolke::fCL
private

Definition at line 37 of file TRolke.h.

## ◆ fLowerLimit

 Double_t TRolke::fLowerLimit
private

Definition at line 39 of file TRolke.h.

## ◆ fNumWarningsDeprecated1

 Int_t TRolke::fNumWarningsDeprecated1
private

Definition at line 42 of file TRolke.h.

## ◆ fNumWarningsDeprecated2

 Int_t TRolke::fNumWarningsDeprecated2
private

Definition at line 43 of file TRolke.h.

## ◆ fUpperLimit

 Double_t TRolke::fUpperLimit
private

Definition at line 38 of file TRolke.h.

Libraries for TRolke: [legend]

The documentation for this class was generated from the following files:
m
auto * m
Definition: textangle.C:8
e
#define e(i)
Definition: RSha256.hxx:103
RooStats::HistFactory::Constraint::Poisson
@ Poisson
Definition: Systematics.h:25
estimate
REAL estimate(int elen, REAL *e)
Definition: triangle.c:5087
x
Double_t x[n]
Definition: legend1.C:17
TMath::Binomial
Double_t Binomial(Int_t n, Int_t k)
Calculate the binomial coefficient n over k.
Definition: TMath.cxx:2083
b
#define b(i)
Definition: RSha256.hxx:100
RooFit::Efficiency
RooCmdArg Efficiency(const RooCategory &cat)
Definition: RooGlobalFunc.cxx:93
RooStats::HistFactory::Constraint::Gaussian
@ Gaussian
Definition: Systematics.h:25
y
Double_t y[n]
Definition: legend1.C:17