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

m

auto * m

Definition: textangle.C:8

For the case of known background expectation or known efficiency:

e = true efficiency (considered known)

b = background expectation value (considered known)

b

#define b(i)

Definition: RSha256.hxx:100

e

#define e(i)

Definition: RSha256.hxx:103

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?

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.
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 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 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 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...

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...

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)

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]

Constructor & Destructor Documentation

◆ 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.

Member Function Documentation

◆ 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.

Member Data Documentation

◆ 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]

TRolke implements the following Models

Parameters and further explanation

For all models:

For Poisson background measurements (sideband or MC):

For Gaussian efficiency or background:

For Binomial signal efficiency:

For the case of known background expectation or known efficiency:

Should I use TRolke, TFeldmanCousins, TLimit?

Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ TRolke()

◆ ~TRolke()

Member Function Documentation

◆ CalculateInterval()

◆ ComputeInterval()

◆ EvalLikeMod1()

◆ EvalLikeMod2()

◆ EvalLikeMod3()

◆ EvalLikeMod4()

◆ EvalLikeMod5()

◆ EvalLikeMod6()

◆ EvalLikeMod7()

◆ EvalMonomial()

◆ EvalPolynomial()

◆ GetBackground()

◆ GetBounding()

◆ GetCL()

◆ GetCriticalNumber()

◆ GetLimits()

◆ GetLimitsML()

◆ GetLimitsQuantile()

◆ GetLowerLimit()

◆ GetSensitivity()

◆ GetUpperLimit()

◆ Interval()

◆ LikeGradMod1()

◆ Likelihood()

◆ LikeMod1()

◆ LikeMod2()

◆ LikeMod3()

◆ LikeMod4()

◆ LikeMod5()

◆ LikeMod6()

◆ LikeMod7()

◆ LogFactorial()

◆ Print()

◆ ProfLikeMod1()

◆ SetBounding()

◆ SetCL()

◆ SetCLSigmas()

◆ SetGaussBkgGaussEff()

◆ SetGaussBkgKnownEff()

◆ SetKnownBkgBinomEff()

◆ SetKnownBkgGaussEff()

◆ SetModelParameters() [1/2]

◆ SetModelParameters() [2/2]

◆ SetPoissonBkgBinomEff()

◆ SetPoissonBkgGaussEff()

◆ SetPoissonBkgKnownEff()

◆ SetSwitch()

Member Data Documentation

◆ f_b

◆ f_bm

◆ f_e

◆ f_em

◆ f_m

◆ f_mid

◆ f_sdb

◆ f_sde

◆ f_tau

◆ f_x

◆ f_y

◆ f_z

◆ fBounding

◆ fCL

◆ fLowerLimit