BayesianCalculator is a concrete implementation of IntervalCalculator, providing the computation of a credible interval using a Bayesian method.

The class works only for one single parameter of interest and it integrates the likelihood function with the given prior probability density function to compute the posterior probability. The result of the class is a one dimensional interval (class SimpleInterval ), which is obtained from inverting the cumulative posterior distribution. This calculator works then only for model with a single parameter of interest. The model can instead have several nuisance parameters which are integrated (marginalized) in the computation of the posterior function. The intergration and normalization of the posterior is computed using numerical integration methods provided by ROOT. See the MCMCCalculator for model with multiple parameters of interest.

The interface allows one to construct the class by passing the data set, probability density function for the model, the prior functions and then the parameter of interest to scan. The nuisance parameters can also be passed to be marginalized when computing the posterior. Alternatively, the class can be constructed by passing the data and the ModelConfig containing all the needed information (model pdf, prior pdf, parameter of interest, nuisance parameters, etc..)

After configuring the calculator, one only needs to ask GetInterval(), which will return an SimpleInterval object. By default the extrem of the integral are obtained by inverting directly the cumulative posterior distribution. By using the method SetScanOfPosterior(nbins) the interval is then obtained by scanning the posterior function in the given number of points. The firts method is in general faster but it requires an integration one extra dimension ( in the poi in addition to the nuisance parameters), therefore in some case it can be less robust.

The class can also return the posterior function (method GetPosteriorFunction) or if needed the normalized posterior function (the posterior pdf) (method GetPosteriorPdf). A posterior plot is also obtained using the GetPosteriorPlot method.

The class allows to use different integration methods for integrating in (marginalizing) the nuisances and in the poi. All the numerical integration methods of ROOT can be used via the method SetIntegrationType (see more in the documentation of this method).

Calculator estimating a credible interval using the Bayesian procedure. The calculator computes given the model the posterior distribution and estimates the credible interval from the given function.

Definition at line 84 of file BayesianCalculator.h.

Public Member Functions
	BayesianCalculator ()
	constructor More...

	BayesianCalculator (RooAbsData &data, RooAbsPdf &pdf, const RooArgSet &POI, RooAbsPdf &priorPdf, const RooArgSet *nuisanceParameters=0)

	BayesianCalculator (RooAbsData &data, ModelConfig &model)

virtual	~BayesianCalculator ()
	destructor More...

RooPlot *	GetPosteriorPlot (bool norm=false, double precision=0.01) const
	get the plot with option to get it normalized More...

RooAbsPdf *	GetPosteriorPdf () const
	return posterior pdf (object is managed by the BayesianCalculator class) More...

RooAbsReal *	GetPosteriorFunction () const
	return posterior function (object is managed by the BayesianCalculator class) More...

virtual SimpleInterval *	GetInterval () const
	compute the interval. More...

virtual void	SetData (RooAbsData &data)
	Set the DataSet ( add to the the workspace if not already there ?) More...

virtual void	SetModel (const ModelConfig &model)
	set the model via the ModelConfig More...

virtual void	SetParameters (const RooArgSet &set)
	specify the parameters of interest in the interval More...

virtual void	SetNuisanceParameters (const RooArgSet &set)
	specify the nuisance parameters (eg. the rest of the parameters) More...

virtual void	SetPriorPdf (RooAbsPdf &pdf)
	Set only the Prior Pdf. More...

virtual void	SetConditionalObservables (const RooArgSet &set)
	set the conditional observables which will be used when creating the NLL so the pdf's will not be normalized on the conditional observables when computing the NLL More...

virtual void	SetTestSize (Double_t size)
	set the size of the test (rate of Type I error) ( Eg. 0.05 for a 95% Confidence Interval) More...

virtual void	SetConfidenceLevel (Double_t cl)
	set the confidence level for the interval (eg. 0.95 for a 95% Confidence Interval) More...

virtual Double_t	Size () const
	Get the size of the test (eg. rate of Type I error) More...

virtual Double_t	ConfidenceLevel () const
	Get the Confidence level for the test. More...

void	SetLeftSideTailFraction (Double_t leftSideFraction)
	set the fraction of probability content on the left tail Central limits use 0.5 (default case) for upper limits it is 0 and 1 for lower limit For shortest intervals a negative value (i.e. More...

void	SetShortestInterval ()
	set the Bayesian calculator to compute the shorest interval (default is central interval) to switch off SetLeftSideTailFraction to the rght value More...

void	SetBrfPrecision (double precision)
	set the precision of the Root Finder More...

void	SetScanOfPosterior (int nbin=100)
	use directly the approximate posterior function obtained by binning it in nbins by default the cdf is used by integrating the posterior if a value of nbin <= 0 the cdf function will be used More...

virtual void	SetNumIters (Int_t numIters)
	set the number of iterations when running a MC integration algorithm If not set use default algorithmic values In case of ToyMC sampling of the nuisance the value is 100 In case of using the GSL MCintegrations types the default value is defined in ROOT::Math::IntegratorMultiDimOptions::DefaultNCalls() More...

void	SetIntegrationType (const char *type)
	set the integration type (possible type are) : More...

double	GetMode () const
	return the mode (most probable value of the posterior function) More...

void	ForceNuisancePdf (RooAbsPdf &pdf)
	force the nuisance pdf when using the toy mc sampling More...

Public Member Functions inherited from RooStats::IntervalCalculator
virtual	~IntervalCalculator ()

Public Member Functions inherited from TNamed
	TNamed ()

	TNamed (const char name, const char title)

	TNamed (const TString &name, const TString &title)

	TNamed (const TNamed &named)

TNamed &	operator= (const TNamed &rhs)
	TNamed assignment operator. More...

virtual	~TNamed ()

virtual void	Clear (Option_t *option="")
	Set name and title to empty strings (""). More...

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 two TNamed objects. More...

virtual void	Copy (TObject &named) const
	Copy this to obj. More...

virtual void	FillBuffer (char *&buffer)
	Encode TNamed into output buffer. More...

virtual const char *	GetName () const
	Returns name of object. More...

virtual const char *	GetTitle () const
	Returns title of object. More...

virtual ULong_t	Hash () const
	Return hash value for this object. More...

virtual Bool_t	IsSortable () const

virtual void	SetName (const char *name)
	Change (i.e. More...

virtual void	SetNameTitle (const char name, const char title)
	Change (i.e. set) all the TNamed parameters (name and title). More...

virtual void	SetTitle (const char *title="")
	Change (i.e. set) the title of the TNamed. More...

virtual void	ls (Option_t *option="") const
	List TNamed name and title. More...

virtual void	Print (Option_t *option="") const
	Print TNamed name and title. More...

virtual Int_t	Sizeof () const
	Return size of the TNamed part of the TObject. More...

Public Member Functions inherited from TObject
	TObject ()

	TObject (const TObject &object)
	TObject copy ctor. More...

TObject &	operator= (const TObject &rhs)
	TObject assignment operator. More...

virtual	~TObject ()
	TObject destructor. 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	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	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 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 UInt_t	GetUniqueID () const
	Return the unique object id. More...

virtual const char *	GetIconName () const
	Returns mime type name of object. More...

virtual Option_t *	GetOption () const

virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py). More...

virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out. 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...

virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More...

virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory). More...

Bool_t	IsOnHeap () const

Bool_t	IsZombie () const

virtual Bool_t	Notify ()
	This method must be overridden to handle object notification. 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...

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...

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	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. 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...

void *	operator new (size_t sz)

void *	operator new[] (size_t sz)

void *	operator new (size_t sz, void *vp)

void *	operator new[] (size_t sz, void *vp)

void	operator delete (void *ptr)
	Operator delete. More...

void	operator delete[] (void *ptr)
	Operator delete []. 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)

void	ResetBit (UInt_t f)

Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

void	InvertBit (UInt_t f)

virtual void	Info (const char method, const char msgfmt,...) const
	Issue info message. More...

virtual void	Warning (const char method, const char msgfmt,...) const
	Issue warning message. More...

virtual void	Error (const char method, const char msgfmt,...) const
	Issue error message. More...

virtual void	SysError (const char method, const char msgfmt,...) const
	Issue system error message. More...

virtual void	Fatal (const char method, const char msgfmt,...) const
	Issue fatal error message. 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...

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...

void	Obsolete (const char method, const char asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete. More...

Protected Member Functions
void	ClearAll () const

void	ApproximatePosterior () const

void	ComputeIntervalFromApproxPosterior (double c1, double c2) const

void	ComputeIntervalFromCdf (double c1, double c2) const

void	ComputeIntervalUsingRooFit (double c1, double c2) const

void	ComputeShortestInterval () const

Protected Member Functions inherited from TObject
void	MakeZombie ()

virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected). More...

Private Attributes
RooAbsData *	fData

RooAbsPdf *	fPdf

RooArgSet	fPOI

RooAbsPdf *	fPriorPdf

RooAbsPdf *	fNuisancePdf

RooArgSet	fNuisanceParameters

RooArgSet	fConditionalObs

RooAbsPdf *	fProductPdf

RooAbsReal *	fLogLike

RooAbsReal *	fLikelihood

RooAbsReal *	fIntegratedLikelihood

RooAbsPdf *	fPosteriorPdf

ROOT::Math::IGenFunction *	fPosteriorFunction

TF1 *	fApproxPosterior

Double_t	fLower

Double_t	fUpper

Double_t	fNLLMin

double	fSize

double	fLeftSideFraction

double	fBrfPrecision

int	fNScanBins

int	fNumIterations

Bool_t	fValidInterval

TString	fIntegrationType

Additional Inherited Members
Public Types inherited from TObject
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) }

enum	{ kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kBitMask = 0x00ffffff }

enum	{ kSingleKey = BIT(0), kOverwrite = BIT(1), kWriteDelete = BIT(2) }

Static Public Member Functions inherited from TObject
static Long_t	GetDtorOnly ()
	Return destructor only flag. More...

static void	SetDtorOnly (void *obj)
	Set destructor only flag. More...

static Bool_t	GetObjectStat ()
	Get status of object stat flag. More...

static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable. More...

Protected Attributes inherited from TNamed
TString	fName

TString	fTitle

#include <RooStats/BayesianCalculator.h>

Inheritance diagram for RooStats::BayesianCalculator:

Collaboration diagram for RooStats::BayesianCalculator:

Constructor & Destructor Documentation

RooStats::BayesianCalculator::BayesianCalculator ( )

constructor

Definition at line 606 of file BayesianCalculator.cxx.

RooStats::BayesianCalculator::BayesianCalculator	(	RooAbsData &	data,
		RooAbsPdf &	pdf,
		const RooArgSet &	POI,
		RooAbsPdf &	priorPdf,
		const RooArgSet *	nuisanceParameters = `0`
	)

Definition at line 624 of file BayesianCalculator.cxx.

RooStats::BayesianCalculator::BayesianCalculator	(	RooAbsData &	data,
		ModelConfig &	model
	)

Definition at line 654 of file BayesianCalculator.cxx.

RooStats::BayesianCalculator::~BayesianCalculator ( )

virtual

destructor

Definition at line 676 of file BayesianCalculator.cxx.

Member Function Documentation

void RooStats::BayesianCalculator::ApproximatePosterior ( ) const

protected

Definition at line 1254 of file BayesianCalculator.cxx.

Referenced by ComputeIntervalFromApproxPosterior(), ComputeShortestInterval(), GetMode(), and GetPosteriorPlot().

void RooStats::BayesianCalculator::ClearAll ( void ) const

protected

Definition at line 682 of file BayesianCalculator.cxx.

Referenced by SetData(), SetModel(), and ~BayesianCalculator().

void RooStats::BayesianCalculator::ComputeIntervalFromApproxPosterior	(	double	c1,
		double	c2
	)		const

protected

Definition at line 1301 of file BayesianCalculator.cxx.

Referenced by GetInterval().

void RooStats::BayesianCalculator::ComputeIntervalFromCdf	(	double	c1,
		double	c2
	)		const

protected

Definition at line 1184 of file BayesianCalculator.cxx.

Referenced by GetInterval().

void RooStats::BayesianCalculator::ComputeIntervalUsingRooFit	(	double	c1,
		double	c2
	)		const

protected

Definition at line 1134 of file BayesianCalculator.cxx.

Referenced by GetInterval().

void RooStats::BayesianCalculator::ComputeShortestInterval ( ) const

protected

Definition at line 1319 of file BayesianCalculator.cxx.

Referenced by GetInterval().

virtual Double_t RooStats::BayesianCalculator::ConfidenceLevel ( ) const

inlinevirtual

Get the Confidence level for the test.

Implements RooStats::IntervalCalculator.

Definition at line 148 of file BayesianCalculator.h.

Referenced by GetInterval().

void RooStats::BayesianCalculator::ForceNuisancePdf ( RooAbsPdf & pdf )

inline

force the nuisance pdf when using the toy mc sampling

Definition at line 182 of file BayesianCalculator.h.

SimpleInterval * RooStats::BayesianCalculator::GetInterval ( ) const

virtual

compute the interval.

By Default a central interval is computed By using SetLeftTileFraction can control if central/ upper/lower interval For shortest interval use SetShortestInterval(true)

Implements RooStats::IntervalCalculator.

Definition at line 1030 of file BayesianCalculator.cxx.

Referenced by GetPosteriorPlot().

double RooStats::BayesianCalculator::GetMode ( ) const

return the mode (most probable value of the posterior function)

Definition at line 1121 of file BayesianCalculator.cxx.

RooAbsReal * RooStats::BayesianCalculator::GetPosteriorFunction ( ) const

return posterior function (object is managed by the BayesianCalculator class)

Definition at line 726 of file BayesianCalculator.cxx.

Referenced by ApproximatePosterior(), ComputeIntervalFromCdf(), GetInterval(), GetPosteriorPdf(), and GetPosteriorPlot().

RooAbsPdf * RooStats::BayesianCalculator::GetPosteriorPdf ( ) const

return posterior pdf (object is managed by the BayesianCalculator class)

Definition at line 929 of file BayesianCalculator.cxx.

Referenced by ComputeIntervalUsingRooFit(), and GetPosteriorPlot().

RooPlot * RooStats::BayesianCalculator::GetPosteriorPlot	(	bool	norm = `false`,
		double	precision = `0.01`
	)		const

get the plot with option to get it normalized

Definition at line 948 of file BayesianCalculator.cxx.

void RooStats::BayesianCalculator::SetBrfPrecision ( double precision )

inline

set the precision of the Root Finder

Definition at line 161 of file BayesianCalculator.h.

virtual void RooStats::BayesianCalculator::SetConditionalObservables ( const RooArgSet & set )

inlinevirtual

set the conditional observables which will be used when creating the NLL so the pdf's will not be normalized on the conditional observables when computing the NLL

Definition at line 136 of file BayesianCalculator.h.

virtual void RooStats::BayesianCalculator::SetConfidenceLevel ( Double_t cl )

inlinevirtual

set the confidence level for the interval (eg. 0.95 for a 95% Confidence Interval)

Implements RooStats::IntervalCalculator.

Definition at line 144 of file BayesianCalculator.h.

virtual void RooStats::BayesianCalculator::SetData ( RooAbsData & )

inlinevirtual

Set the DataSet ( add to the the workspace if not already there ?)

Implements RooStats::IntervalCalculator.

Definition at line 116 of file BayesianCalculator.h.

void RooStats::BayesianCalculator::SetIntegrationType ( const char * type )

set the integration type (possible type are) :

Definition at line 992 of file BayesianCalculator.cxx.

void RooStats::BayesianCalculator::SetLeftSideTailFraction ( Double_t leftSideFraction )

inline

set the fraction of probability content on the left tail Central limits use 0.5 (default case) for upper limits it is 0 and 1 for lower limit For shortest intervals a negative value (i.e.

-1) must be given

Definition at line 154 of file BayesianCalculator.h.

void RooStats::BayesianCalculator::SetModel ( const ModelConfig & model )

virtual

set the model via the ModelConfig

Implements RooStats::IntervalCalculator.

Definition at line 703 of file BayesianCalculator.cxx.

Referenced by BayesianCalculator().

virtual void RooStats::BayesianCalculator::SetNuisanceParameters ( const RooArgSet & set )

inlinevirtual

specify the nuisance parameters (eg. the rest of the parameters)

Definition at line 129 of file BayesianCalculator.h.

virtual void RooStats::BayesianCalculator::SetNumIters ( Int_t numIters )

inlinevirtual

set the number of iterations when running a MC integration algorithm If not set use default algorithmic values In case of ToyMC sampling of the nuisance the value is 100 In case of using the GSL MCintegrations types the default value is defined in ROOT::Math::IntegratorMultiDimOptions::DefaultNCalls()

Definition at line 173 of file BayesianCalculator.h.

virtual void RooStats::BayesianCalculator::SetParameters ( const RooArgSet & set )

inlinevirtual

specify the parameters of interest in the interval

Definition at line 126 of file BayesianCalculator.h.

virtual void RooStats::BayesianCalculator::SetPriorPdf ( RooAbsPdf & pdf )

inlinevirtual

Set only the Prior Pdf.

Definition at line 132 of file BayesianCalculator.h.

void RooStats::BayesianCalculator::SetScanOfPosterior ( int nbin = 100 )

inline

use directly the approximate posterior function obtained by binning it in nbins by default the cdf is used by integrating the posterior if a value of nbin <= 0 the cdf function will be used

Definition at line 166 of file BayesianCalculator.h.

void RooStats::BayesianCalculator::SetShortestInterval ( )

inline

set the Bayesian calculator to compute the shorest interval (default is central interval) to switch off SetLeftSideTailFraction to the rght value

Definition at line 158 of file BayesianCalculator.h.

virtual void RooStats::BayesianCalculator::SetTestSize ( Double_t size )

inlinevirtual

set the size of the test (rate of Type I error) ( Eg. 0.05 for a 95% Confidence Interval)

Implements RooStats::IntervalCalculator.

Definition at line 139 of file BayesianCalculator.h.

Referenced by SetConfidenceLevel().

virtual Double_t RooStats::BayesianCalculator::Size ( ) const