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 integration 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 first 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 36 of file BayesianCalculator.h.

Public Member Functions
	BayesianCalculator ()
	default constructor More...

	BayesianCalculator (RooAbsData &data, RooAbsPdf &pdf, const RooArgSet &POI, RooAbsPdf &priorPdf, const RooArgSet *nuisanceParameters=0)
	Constructor from data set, model pdf, parameter of interests and prior pdf If nuisance parameters are given they will be integrated according either to the prior or their constraint term included in the model. More...

	BayesianCalculator (RooAbsData &data, ModelConfig &model)
	Constructor from a data set and a ModelConfig model pdf, poi and nuisances will be taken from the ModelConfig. More...

virtual	~BayesianCalculator ()

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

void	ForceNuisancePdf (RooAbsPdf &pdf)

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

double	GetMode () const
	Returns the value of the parameter for the point in parameter-space that is the most likely. More...

RooAbsReal *	GetPosteriorFunction () const
	Build and return the posterior function (not normalized) as a RooAbsReal the posterior is obtained from the product of the likelihood function and the prior pdf which is then integrated in the nuisance parameters (if existing). More...

RooAbsPdf *	GetPosteriorPdf () const
	Build and return the posterior pdf (i.e posterior function normalized to all range of poi) Note that an extra integration in the POI is required for the normalization NOTE: user must delete the returned object. More...

RooPlot *	GetPosteriorPlot (bool norm=false, double precision=0.01) const
	return a RooPlot with the posterior and the credibility region NOTE: User takes ownership of the returned object More...

void	SetBrfPrecision (double precision)

virtual void	SetConditionalObservables (const RooArgSet &set)

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

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

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

void	SetLeftSideTailFraction (Double_t leftSideFraction)

virtual void	SetModel (const ModelConfig &model)
	set the model to use The model pdf, prior pdf, parameter of interest and nuisances will be taken according to the model More...

virtual void	SetNuisanceParameters (const RooArgSet &set)

virtual void	SetNumIters (Int_t numIters)

virtual void	SetParameters (const RooArgSet &set)

virtual void	SetPriorPdf (RooAbsPdf &pdf)

void	SetScanOfPosterior (int nbin=100)

void	SetShortestInterval ()

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

virtual Double_t	Size () const
	Get the size of the test (eg. rate of Type I error) 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 copy ctor. 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	ls (Option_t *option="") const
	List TNamed name and title. More...

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

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

virtual void	SetName (const char *name)
	Set the name of the TNamed. More...

virtual void	SetNameTitle (const char name, const char title)
	Set all the TNamed parameters (name and title). More...

virtual void	SetTitle (const char *title="")
	Set the title of the TNamed. More...

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

Public Member Functions inherited from TObject
	TObject ()
	TObject constructor. More...

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

virtual	~TObject ()
	TObject destructor. More...

void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract. More...

virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad. More...

virtual void	Browse (TBrowser *b)
	Browse object. May be overridden for another default action. More...

virtual const char *	ClassName () const
	Returns name of class to which the object belongs. More...

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

virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname". More...

virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl. More...

virtual void	Inspect () const
	Dump contents of this object in a graphics canvas. More...

void	InvertBit (UInt_t f)

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

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

Bool_t	IsOnHeap () const

Bool_t	IsZombie () const

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 Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory. More...

virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list. More...

void	ResetBit (UInt_t f)

virtual void	SaveAs (const char filename="", Option_t option="") const
	Save this object in the file specified by filename. More...

virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save a primitive as a C++ statement(s) on output stream "out". More...

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

void	SetBit (UInt_t f)

virtual void	SetDrawOption (Option_t *option="")
	Set drawing option for object. More...

virtual void	SetUniqueID (UInt_t uid)
	Set the unique object id. More...

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

Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

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

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

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory. More...

Protected Member Functions
void	ApproximatePosterior () const
	approximate posterior in nbins using a TF1 scan the poi values and evaluate the posterior at each point and save the result in a cloned TF1 For each point the posterior is evaluated by integrating the nuisance parameters More...

void	ClearAll () const
	clear all cached pdf objects More...

void	ComputeIntervalFromApproxPosterior (double c1, double c2) const
	compute the interval using the approximate posterior function More...

void	ComputeIntervalFromCdf (double c1, double c2) const
	internal function compute the interval using Cdf integration More...

void	ComputeIntervalUsingRooFit (double c1, double c2) const
	internal function compute the interval using RooFit More...

void	ComputeShortestInterval () const
	compute the shortest interval More...

Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected). More...

void	MakeZombie ()

Private Attributes
TF1 *	fApproxPosterior

double	fBrfPrecision

RooArgSet	fConditionalObs

RooAbsData *	fData

RooAbsReal *	fIntegratedLikelihood

TString	fIntegrationType

double	fLeftSideFraction

RooAbsReal *	fLikelihood

RooAbsReal *	fLogLike

Double_t	fLower

Double_t	fNLLMin

int	fNScanBins

RooArgSet	fNuisanceParameters

RooAbsPdf *	fNuisancePdf

int	fNumIterations

RooAbsPdf *	fPdf

RooArgSet	fPOI

ROOT::Math::IGenFunction *	fPosteriorFunction

RooAbsPdf *	fPosteriorPdf

RooAbsPdf *	fPriorPdf

RooAbsPdf *	fProductPdf

double	fSize

Double_t	fUpper

Bool_t	fValidInterval

Additional Inherited Members
Public Types inherited from TObject
enum	{ kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kBitMask = 0x00ffffff }

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

enum	EStatusBits { kCanDelete = BIT(0), kMustCleanup = BIT(3), kObjInCanvas = BIT(3), kIsReferenced = BIT(4), kHasUUID = BIT(5), kCannotPick = BIT(6), kNoContextMenu = BIT(8), kInvalidObject = BIT(13) }

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

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

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

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

Protected Attributes inherited from TNamed
TString	fName

TString	fTitle

#include <RooStats/BayesianCalculator.h>

Inheritance diagram for RooStats::BayesianCalculator:

[legend]

Constructor & Destructor Documentation

◆ BayesianCalculator() [1/3]

RooStats::BayesianCalculator::BayesianCalculator ( )

default constructor

Definition at line 645 of file BayesianCalculator.cxx.

◆ BayesianCalculator() [2/3]

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

Constructor from data set, model pdf, parameter of interests and prior pdf If nuisance parameters are given they will be integrated according either to the prior or their constraint term included in the model.

Definition at line 667 of file BayesianCalculator.cxx.

◆ BayesianCalculator() [3/3]

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

Constructor from a data set and a ModelConfig model pdf, poi and nuisances will be taken from the ModelConfig.

Definition at line 698 of file BayesianCalculator.cxx.

◆ ~BayesianCalculator()

RooStats::BayesianCalculator::~BayesianCalculator ( )

virtual

Definition at line 718 of file BayesianCalculator.cxx.

Member Function Documentation

◆ ApproximatePosterior()

void RooStats::BayesianCalculator::ApproximatePosterior ( ) const

protected

approximate posterior in nbins using a TF1 scan the poi values and evaluate the posterior at each point and save the result in a cloned TF1 For each point the posterior is evaluated by integrating the nuisance parameters

Definition at line 1320 of file BayesianCalculator.cxx.

◆ ClearAll()

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

protected

clear all cached pdf objects

Definition at line 727 of file BayesianCalculator.cxx.

◆ ComputeIntervalFromApproxPosterior()

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

protected

compute the interval using the approximate posterior function

Definition at line 1365 of file BayesianCalculator.cxx.

◆ ComputeIntervalFromCdf()

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

protected

internal function compute the interval using Cdf integration

Definition at line 1244 of file BayesianCalculator.cxx.

◆ ComputeIntervalUsingRooFit()

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

protected

internal function compute the interval using RooFit

Definition at line 1192 of file BayesianCalculator.cxx.

◆ ComputeShortestInterval()

void RooStats::BayesianCalculator::ComputeShortestInterval ( ) const

protected

compute the shortest interval

Definition at line 1385 of file BayesianCalculator.cxx.

◆ ConfidenceLevel()

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

inlinevirtual

Get the Confidence level for the test.

Implements RooStats::IntervalCalculator.

Definition at line 100 of file BayesianCalculator.h.

◆ ForceNuisancePdf()

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

inline

Definition at line 134 of file BayesianCalculator.h.

◆ GetInterval()

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

virtual

Compute the interval.

By Default a central interval is computed and the result is a SimpleInterval object.

Using the method (to be called before SetInterval) SetLeftSideTailFraction the user can choose the type of interval. By default the returned interval is a central interval with the confidence level specified previously in the constructor ( LeftSideTailFraction = 0.5).

For lower limit use SetLeftSideTailFraction = 1
For upper limit use SetLeftSideTailFraction = 0
for shortest intervals use SetLeftSideTailFraction = -1 or call the method SetShortestInterval()

NOTE: The BayesianCalculator covers only the case with one single parameter of interest

NOTE: User takes ownership of the returned object

Implements RooStats::IntervalCalculator.

Definition at line 1094 of file BayesianCalculator.cxx.

◆ GetMode()

double RooStats::BayesianCalculator::GetMode ( ) const

Returns the value of the parameter for the point in parameter-space that is the most likely.

How do we do if there are points that are equi-probable? use approximate posterior t.b.d use real function to find the mode

Definition at line 1181 of file BayesianCalculator.cxx.

◆ GetPosteriorFunction()

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

Build and return the posterior function (not normalized) as a RooAbsReal the posterior is obtained from the product of the likelihood function and the prior pdf which is then integrated in the nuisance parameters (if existing).

A prior function for the nuisance can be specified either in the prior pdf object or in the model itself. If no prior nuisance is specified, but prior parameters are then the integration is performed assuming a flat prior for the nuisance parameters.

NOTE: the return object is managed by the class, users do not need to delete it

Definition at line 780 of file BayesianCalculator.cxx.

◆ GetPosteriorPdf()

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

Build and return the posterior pdf (i.e posterior function normalized to all range of poi) Note that an extra integration in the POI is required for the normalization NOTE: user must delete the returned object.

Definition at line 981 of file BayesianCalculator.cxx.

◆ GetPosteriorPlot()

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

return a RooPlot with the posterior and the credibility region NOTE: User takes ownership of the returned object

Definition at line 1000 of file BayesianCalculator.cxx.

◆ SetBrfPrecision()

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

inline

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

set the integration type (possible type are) :

1D integration ( used when only one nuisance and when the posterior is scanned): adaptive , gauss, nonadaptive
multidim:
- ADAPTIVE, adaptive numerical integration The parameter numIters (settable with SetNumIters) is the max number of function calls. It can be reduced to make the integration faster but it will be difficult to reach the required tolerance
- VEGAS MC integration method based on importance sampling - numIters is number of function calls Extra Vegas parameter can be set using IntegratorMultiDimOptions class
- MISER MC integration method based on stratified sampling See also http://en.wikipedia.org/wiki/Monte_Carlo_integration for VEGAS and MISER description
- PLAIN simple MC integration method, where the max number of calls can be specified using SetNumIters(numIters)

Extra integration types are:

TOYMC: evaluate posterior by generating toy MC for the nuisance parameters. It is a MC integration, where the function is sampled according to the nuisance. It is convenient to use when all the nuisance are uncorrelated and it is efficient to generate them The toy are generated by default for each poi values (this method has been proposed and provided by J.P Chou)
1-TOYMC : same method as before but in this case the toys are generated only one time and then used for each poi value. It can be convenient when the generation time is much larger than the evaluation time, otherwise it is recommended to re-generate the toy for each poi scanned point of the posterior function
ROOFIT: use roofit default integration methods which will produce a nested integral (not recommended for more than 1 nuisance parameters)

Definition at line 1072 of file BayesianCalculator.cxx.

◆ SetLeftSideTailFraction()

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

inline

Definition at line 106 of file BayesianCalculator.h.

◆ SetModel()

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

virtual

Definition at line 91 of file BayesianCalculator.h.

◆ Size()

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

inlinevirtual

Get the size of the test (eg. rate of Type I error)

Bool_t RooStats::BayesianCalculator::fValidInterval

mutableprivate

Definition at line 179 of file BayesianCalculator.h.

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

roofit/roostats/inc/RooStats/BayesianCalculator.h
roofit/roostats/src/BayesianCalculator.cxx

Public Member Functions

Protected Member Functions

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ BayesianCalculator() [1/3]

◆ BayesianCalculator() [2/3]

◆ BayesianCalculator() [3/3]

◆ ~BayesianCalculator()

Member Function Documentation

◆ ApproximatePosterior()

◆ ClearAll()

◆ ComputeIntervalFromApproxPosterior()

◆ ComputeIntervalFromCdf()

◆ ComputeIntervalUsingRooFit()

◆ ComputeShortestInterval()

◆ ConfidenceLevel()

◆ ForceNuisancePdf()

◆ GetInterval()

◆ GetMode()

◆ GetPosteriorFunction()

◆ GetPosteriorPdf()

◆ GetPosteriorPlot()

◆ SetBrfPrecision()

◆ SetConditionalObservables()

◆ SetConfidenceLevel()

◆ SetData()

◆ SetIntegrationType()

◆ SetLeftSideTailFraction()

◆ SetModel()

◆ SetNuisanceParameters()

◆ SetNumIters()

◆ SetParameters()

◆ SetPriorPdf()

◆ SetScanOfPosterior()

◆ SetShortestInterval()

◆ SetTestSize()

◆ Size()

Member Data Documentation

◆ fApproxPosterior

◆ fBrfPrecision

◆ fConditionalObs

◆ fData

◆ fIntegratedLikelihood

◆ fIntegrationType

◆ fLeftSideFraction

◆ fLikelihood

◆ fLogLike

◆ fLower

◆ fNLLMin

◆ fNScanBins

◆ fNuisanceParameters

◆ fNuisancePdf

◆ fNumIterations

◆ fPdf

◆ fPOI

◆ fPosteriorFunction

◆ fPosteriorPdf

◆ fPriorPdf

◆ fProductPdf

◆ fSize

◆ fUpper

◆ fValidInterval