ROOT   Reference Guide
RooStats::BayesianCalculator Class Reference

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 37 of file BayesianCalculator.h.

## Public Member Functions

BayesianCalculator ()
constructor 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...

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 () override
destructor More...

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

void ForceNuisancePdf (RooAbsPdf &pdf)

SimpleIntervalGetInterval () const override
compute the interval. More...

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

RooAbsRealGetPosteriorFunction () const
return posterior function (object is managed by the BayesianCalculator class) More...

TH1GetPosteriorHistogram () const
return the approximate posterior as histogram (TH1 object). Note the object is managed by the BayesianCalculator class More...

RooAbsPdfGetPosteriorPdf () const
return posterior pdf (object is managed by the user) More...

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

TClassIsA () const override

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

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

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

virtual void SetGlobalObservables (const RooArgSet &set)
set the global observables which will be used when creating the NLL so the constraint pdf's will be normalized correctly on the global observables when computing the NLL More...

void SetIntegrationType (const char *type)
set the integration type (possible type are) : 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 SetModel (const ModelConfig &model) override
set the model via the ModelConfig More...

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

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

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

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

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

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

void Streamer (TBuffer &) override
Stream an object of class TObject. More...

void StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

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

virtual Double_t ConfidenceLevel () const =0
Get the Confidence level for the test. More...

virtual ConfIntervalGetInterval () const =0
Main interface to get a ConfInterval, pure virtual. More...

virtual TClassIsA () const

virtual void SetConfidenceLevel (Double_t cl)=0
set the confidence level for the interval (e.g. 0.95 for a 95% Confidence Interval) More...

virtual void SetData (RooAbsData &)=0
Set the DataSet ( add to the the workspace if not already there ?) More...

virtual void SetModel (const ModelConfig &)=0
Set the Model. More...

virtual void SetTestSize (Double_t size)=0
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 =0
Get the size of the test (eg. rate of Type I error) More...

virtual void Streamer (TBuffer &)

void StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Public Member Functions inherited from TNamed
TNamed ()

TNamed (const char *name, const char *title)

TNamed (const TNamed &named)
TNamed copy ctor. More...

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

virtual ~TNamed ()
TNamed destructor. More...

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

TObjectClone (const char *newname="") const override
Make a clone of an object using the Streamer facility. More...

Int_t Compare (const TObject *obj) const override
Compare two TNamed objects. More...

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

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

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

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

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

TClassIsA () const override

Bool_t IsSortable () const override

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

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

void Print (Option_t *option="") const override
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...

void Streamer (TBuffer &) override
Stream an object of class TObject. More...

void StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

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...

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
Must be redefined in derived classes. More...

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 TClassIsA () const

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)

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 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 Streamer (TBuffer &)
Stream an object of class TObject. More...

void StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

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...

## Static Public Member Functions

static TClassClass ()

static const char * Class_Name ()

static Version_t Class_Version ()

static const char * DeclFileName ()

Static Public Member Functions inherited from RooStats::IntervalCalculator
static TClassClass ()

static const char * Class_Name ()

static Version_t Class_Version ()

static const char * DeclFileName ()

Static Public Member Functions inherited from TNamed
static TClassClass ()

static const char * Class_Name ()

static Version_t Class_Version ()

static const char * DeclFileName ()

Static Public Member Functions inherited from TObject
static TClassClass ()

static const char * Class_Name ()

static Version_t Class_Version ()

static const char * DeclFileName ()

static Longptr_t GetDtorOnly ()
Return destructor only flag. More...

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

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

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

## Protected Member Functions

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 from the histogram representing the posterior 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

TF1fApproxPosterior
TF1 representing the scanned posterior function. More...

double fBrfPrecision
root finder precision More...

RooArgSet fConditionalObs
conditional observables More...

RooAbsDatafData
data set More...

RooArgSet fGlobalObs
global observables More...

RooAbsRealfIntegratedLikelihood
integrated likelihood function, i.e - unnormalized posterior function More...

TString fIntegrationType

double fLeftSideFraction
fraction of probability content on left side of interval More...

RooAbsRealfLikelihood
internal pointer to likelihood function More...

RooAbsRealfLogLike
internal pointer to log likelihood function More...

Double_t fLower
computer lower interval bound More...

Double_t fNLLMin
minimum value of Nll More...

int fNScanBins
number of bins to scan, if = -1 no scan is done (default) More...

RooArgSet fNuisanceParameters
nuisance parameters More...

RooAbsPdffNuisancePdf
nuisance pdf (needed when using nuisance sampling technique) More...

int fNumIterations
number of iterations (when using ToyMC) More...

RooAbsPdffPdf
model pdf (could contain the nuisance pdf as constraint term) More...

RooArgSet fPOI
POI. More...

ROOT::Math::IGenFunctionfPosteriorFunction
function representing the posterior More...

RooAbsPdffPosteriorPdf
normalized (on the poi) posterior pdf More...

RooAbsPdffPriorPdf
prior pdf (typically for the POI) More...

RooAbsPdffProductPdf
internal pointer to model * prior More...

double fSize
size used for getting the interval More...

Double_t fUpper
upper interval bound More...

Bool_t fValidInterval

Public Types inherited from TObject
enum  {
kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 ,
}

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

enum  EDeprecatedStatusBits { kObjInCanvas = (1ULL << ( 3 )) }

enum  EStatusBits {
kCanDelete = (1ULL << ( 0 )) , kMustCleanup = (1ULL << ( 3 )) , kIsReferenced = (1ULL << ( 4 )) , kHasUUID = (1ULL << ( 5 )) ,
kCannotPick = (1ULL << ( 6 )) , kNoContextMenu = (1ULL << ( 8 )) , kInvalidObject = (1ULL << ( 13 ))
}

Protected Types inherited from TObject
enum  { kOnlyPrepStep = (1ULL << ( 3 )) }

Protected Attributes inherited from TNamed
TString fName

TString fTitle

#include <RooStats/BayesianCalculator.h>

Inheritance diagram for RooStats::BayesianCalculator:
[legend]

## ◆ BayesianCalculator() [1/3]

 RooStats::BayesianCalculator::BayesianCalculator ( )

constructor

default constructor

Definition at line 643 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 665 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 696 of file BayesianCalculator.cxx.

## ◆ ~BayesianCalculator()

 RooStats::BayesianCalculator::~BayesianCalculator ( )
override

destructor

Definition at line 716 of file BayesianCalculator.cxx.

## ◆ 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 1336 of file BayesianCalculator.cxx.

## ◆ Class()

 static TClass * RooStats::BayesianCalculator::Class ( )
static
Returns
TClass describing this class

## ◆ Class_Name()

 static const char * RooStats::BayesianCalculator::Class_Name ( )
static
Returns
Name of this class

## ◆ Class_Version()

 static Version_t RooStats::BayesianCalculator::Class_Version ( )
inlinestatic
Returns
Version of this class

Definition at line 194 of file BayesianCalculator.h.

## ◆ ClearAll()

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

clear all cached pdf objects

Definition at line 725 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 1381 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 1260 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 1208 of file BayesianCalculator.cxx.

## ◆ ComputeShortestInterval()

 void RooStats::BayesianCalculator::ComputeShortestInterval ( ) const
protected

compute the shortest interval from the histogram representing the posterior

Definition at line 1402 of file BayesianCalculator.cxx.

## ◆ ConfidenceLevel()

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

Get the Confidence level for the test.

Implements RooStats::IntervalCalculator.

Definition at line 108 of file BayesianCalculator.h.

## ◆ DeclFileName()

 static const char * RooStats::BayesianCalculator::DeclFileName ( )
inlinestatic
Returns
Name of the file containing the class declaration

Definition at line 194 of file BayesianCalculator.h.

## ◆ ForceNuisancePdf()

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

Definition at line 142 of file BayesianCalculator.h.

## ◆ GetInterval()

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

compute the interval.

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)

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 1110 of file BayesianCalculator.cxx.

## ◆ GetMode()

 double RooStats::BayesianCalculator::GetMode ( ) const

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

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 1197 of file BayesianCalculator.cxx.

## ◆ GetPosteriorFunction()

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

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

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 BayesianCalculator class, users do not need to delete it, but the object will be deleted when the BayesiabCalculator object is deleted

Definition at line 781 of file BayesianCalculator.cxx.

## ◆ GetPosteriorHistogram()

 TH1 * RooStats::BayesianCalculator::GetPosteriorHistogram ( ) const

return the approximate posterior as histogram (TH1 object). Note the object is managed by the BayesianCalculator class

When am approximate posterior is computed binninig the parameter of interest (poi) range (see SetScanOfPosteriors) an histogram is created and can be returned to the user A nullptr is instead returned when the posterior is computed without binning the poi.

NOTE: the returned object is managed by the BayesianCalculator class, if the user wants to take ownership of the returned histogram, he needs to clone or copy the return object.

Definition at line 1006 of file BayesianCalculator.cxx.

## ◆ GetPosteriorPdf()

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

return posterior pdf (object is managed by the user)

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 982 of file BayesianCalculator.cxx.

## ◆ GetPosteriorPlot()

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

get the plot with option to get it normalized

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

Definition at line 1016 of file BayesianCalculator.cxx.

## ◆ IsA()

 TClass * RooStats::BayesianCalculator::IsA ( ) const
inlineoverridevirtual
Returns
TClass describing current object

Reimplemented from TNamed.

Definition at line 194 of file BayesianCalculator.h.

## ◆ SetBrfPrecision()

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

set the precision of the Root Finder

Definition at line 121 of file BayesianCalculator.h.

## ◆ SetConditionalObservables()

 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 92 of file BayesianCalculator.h.

## ◆ SetConfidenceLevel()

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

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

Implements RooStats::IntervalCalculator.

Definition at line 104 of file BayesianCalculator.h.

## ◆ SetData()

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

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

Implements RooStats::IntervalCalculator.

Definition at line 72 of file BayesianCalculator.h.

## ◆ SetGlobalObservables()

 virtual void RooStats::BayesianCalculator::SetGlobalObservables ( const RooArgSet & set )
inlinevirtual

set the global observables which will be used when creating the NLL so the constraint pdf's will be normalized correctly on the global observables when computing the NLL

Definition at line 96 of file BayesianCalculator.h.

## ◆ SetIntegrationType()

 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 1088 of file BayesianCalculator.cxx.

## ◆ SetLeftSideTailFraction()

 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 114 of file BayesianCalculator.h.

## ◆ SetModel()

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

set the model via the ModelConfig

set the model to use The model pdf, prior pdf, parameter of interest and nuisances will be taken according to the model

Implements RooStats::IntervalCalculator.

Definition at line 750 of file BayesianCalculator.cxx.

## ◆ SetNuisanceParameters()

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

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

Definition at line 85 of file BayesianCalculator.h.

## ◆ SetNumIters()

 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 133 of file BayesianCalculator.h.

## ◆ SetParameters()

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

specify the parameters of interest in the interval

Definition at line 82 of file BayesianCalculator.h.

## ◆ SetPriorPdf()

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

Set only the Prior Pdf.

Definition at line 88 of file BayesianCalculator.h.

## ◆ SetScanOfPosterior()

 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 126 of file BayesianCalculator.h.

## ◆ SetShortestInterval()

 void RooStats::BayesianCalculator::SetShortestInterval ( )
inline

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

Definition at line 118 of file BayesianCalculator.h.

## ◆ SetTestSize()

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

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 99 of file BayesianCalculator.h.

## ◆ Size()

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

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

Implements RooStats::IntervalCalculator.

Definition at line 106 of file BayesianCalculator.h.

## ◆ Streamer()

 void RooStats::BayesianCalculator::Streamer ( TBuffer & R__b )
overridevirtual

Stream an object of class TObject.

Reimplemented from TNamed.

## ◆ StreamerNVirtual()

 void RooStats::BayesianCalculator::StreamerNVirtual ( TBuffer & ClassDef_StreamerNVirtual_b )
inline

Definition at line 194 of file BayesianCalculator.h.

## ◆ fApproxPosterior

 TF1* RooStats::BayesianCalculator::fApproxPosterior
mutableprivate

TF1 representing the scanned posterior function.

Definition at line 179 of file BayesianCalculator.h.

## ◆ fBrfPrecision

 double RooStats::BayesianCalculator::fBrfPrecision
private

root finder precision

Definition at line 185 of file BayesianCalculator.h.

## ◆ fConditionalObs

 RooArgSet RooStats::BayesianCalculator::fConditionalObs
private

conditional observables

Definition at line 170 of file BayesianCalculator.h.

## ◆ fData

 RooAbsData* RooStats::BayesianCalculator::fData
private

data set

Definition at line 164 of file BayesianCalculator.h.

## ◆ fGlobalObs

 RooArgSet RooStats::BayesianCalculator::fGlobalObs
private

global observables

Definition at line 171 of file BayesianCalculator.h.

## ◆ fIntegratedLikelihood

 RooAbsReal* RooStats::BayesianCalculator::fIntegratedLikelihood
mutableprivate

integrated likelihood function, i.e - unnormalized posterior function

Definition at line 176 of file BayesianCalculator.h.

## ◆ fIntegrationType

 TString RooStats::BayesianCalculator::fIntegrationType
private

Definition at line 190 of file BayesianCalculator.h.

## ◆ fLeftSideFraction

 double RooStats::BayesianCalculator::fLeftSideFraction
private

fraction of probability content on left side of interval

Definition at line 184 of file BayesianCalculator.h.

## ◆ fLikelihood

 RooAbsReal* RooStats::BayesianCalculator::fLikelihood
mutableprivate

internal pointer to likelihood function

Definition at line 175 of file BayesianCalculator.h.

## ◆ fLogLike

 RooAbsReal* RooStats::BayesianCalculator::fLogLike
mutableprivate

internal pointer to log likelihood function

Definition at line 174 of file BayesianCalculator.h.

## ◆ fLower

 Double_t RooStats::BayesianCalculator::fLower
mutableprivate

computer lower interval bound

Definition at line 180 of file BayesianCalculator.h.

## ◆ fNLLMin

 Double_t RooStats::BayesianCalculator::fNLLMin
mutableprivate

minimum value of Nll

Definition at line 182 of file BayesianCalculator.h.

## ◆ fNScanBins

 int RooStats::BayesianCalculator::fNScanBins
mutableprivate

number of bins to scan, if = -1 no scan is done (default)

Definition at line 186 of file BayesianCalculator.h.

## ◆ fNuisanceParameters

 RooArgSet RooStats::BayesianCalculator::fNuisanceParameters
private

nuisance parameters

Definition at line 169 of file BayesianCalculator.h.

## ◆ fNuisancePdf

 RooAbsPdf* RooStats::BayesianCalculator::fNuisancePdf
private

nuisance pdf (needed when using nuisance sampling technique)

Definition at line 168 of file BayesianCalculator.h.

## ◆ fNumIterations

 int RooStats::BayesianCalculator::fNumIterations
private

number of iterations (when using ToyMC)

Definition at line 187 of file BayesianCalculator.h.

## ◆ fPdf

 RooAbsPdf* RooStats::BayesianCalculator::fPdf
private

model pdf (could contain the nuisance pdf as constraint term)

Definition at line 165 of file BayesianCalculator.h.

## ◆ fPOI

 RooArgSet RooStats::BayesianCalculator::fPOI
private

POI.

Definition at line 166 of file BayesianCalculator.h.

## ◆ fPosteriorFunction

 ROOT::Math::IGenFunction* RooStats::BayesianCalculator::fPosteriorFunction
mutableprivate

function representing the posterior

Definition at line 178 of file BayesianCalculator.h.

## ◆ fPosteriorPdf

 RooAbsPdf* RooStats::BayesianCalculator::fPosteriorPdf
mutableprivate

normalized (on the poi) posterior pdf

Definition at line 177 of file BayesianCalculator.h.

## ◆ fPriorPdf

 RooAbsPdf* RooStats::BayesianCalculator::fPriorPdf
private

prior pdf (typically for the POI)

Definition at line 167 of file BayesianCalculator.h.

## ◆ fProductPdf

 RooAbsPdf* RooStats::BayesianCalculator::fProductPdf
mutableprivate

internal pointer to model * prior

Definition at line 173 of file BayesianCalculator.h.

## ◆ fSize

 double RooStats::BayesianCalculator::fSize
private

size used for getting the interval

Definition at line 183 of file BayesianCalculator.h.

## ◆ fUpper

 Double_t RooStats::BayesianCalculator::fUpper
mutableprivate

upper interval bound

Definition at line 181 of file BayesianCalculator.h.

## ◆ fValidInterval

 Bool_t RooStats::BayesianCalculator::fValidInterval
mutableprivate

Definition at line 188 of file BayesianCalculator.h.

Libraries for RooStats::BayesianCalculator:
[legend]

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