KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel > Class Template Reference

Detailed Description

template<class FittingFunction, class FluctuationKernel>
class KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >

Impact parameter distribution reconstruction from experimental data.

Template Parameters

FittingFunction	Class implementing a parameterization of the relationship between mean value of observables as a function of centrality, $\bar{X}(c_b)$
FluctuationKernel	Class implementing fluctuations of the observable according to a given PDF

Implementation of the method of estimating impact parameter distributions for experimental data presented in the articles Das et al., Phys. Rev. C 97, 014905(2018) and Rogly et al., Phys. Rev. C 98, 024902(2018).

The aim is to reproduce the inclusive distribution $P(X)$ of an observable assumed to have a monotonic dependence on impact parameter by adjusting the parameters of a fitting function defined by

$$P(X) = \int P(X|b) P(b) db = \int P(X|c_b) dc_b$$

where $c_b$ is the centrality defined by

$$c_b = \int_0^b P(b) db$$

$P(X|c_b)$ is the probability distribution of the observable as a function of the centrality, which is given by some FluctuationKernel which is a PDF for any value of $X$ given the expected mean $\bar{X}$ and reduced variance $\sigma^2/\bar{X}$.

The FittingFunction class has to provide the functions

double meanX(double c) const
double redVar(double c) const

which describe how $\bar{X}$ and $\sigma^2/\bar{X}$. depend on centrality. It must also provide the following methods:

FittingFunction::FittingFunction()                               default constructor
FittingFunction::FittingFunction(const FittingFunction&)         copy constructor, copy parameter values
constexpr int FittingFunction::npar() const                      number of parameters of function
void FittingFunction::fill_params_from_array(double*)            takes values of parameters from array
void FittingFunction::fill_array_from_params(double*) const      puts values of parameters in array
void FittingFunction::set_par_names(TF1&) const                  set names of parameters in TF1
void FittingFunction::set_initial_parameters(TH1*,TF1&)          set initial values and limits on parameters to fit histogram
void FittingFunction::print_fit_params() const                   set initial values and limits on parameters to fit histogram
void FittingFunction::backup_params() const                      store current values of fit parameters (internally)
void FittingFunction::restore_params() const                     restore previously backed up values of fit parameters
void FittingFunction::normalise_shape_function() const           normalize shape parameters

We provide the following FittingFunctions and FluctuationKernels:

FittingFunction	Function
algebraic_fitting_function	$k(c_b) = (k_{\mathrm{max}}-k_{\mathrm{min}})\left[ 1 - {c_b}^{\alpha}\right]^{\gamma} + k_{\mathrm{min}}$
rogly_fitting_function	$k(c_b) = k_0 \exp{\left(-\sum_{i=1}^{N} a_i c_b^i\right)}$

FluctuationKernel	Distribution	Function
gamma_kernel	Gamma	$f(X) = \frac{1}{\Gamma(k)\theta^k} X^{k-1} \exp{(-X/\theta)}$
BD_kernel	Binomial	$f(X) = \frac{n!}{X!(n-X)!} p^{X}(1-p)^{n-X}$
NBD_kernel	Negative binomial	$f(X) = \frac{(X+n-1)!}{X!(n-1)!} p^{n}(1-p)^{X}$

Example of use

In all of the the following, the namespace prefix KVImpactParameters:: can be dropped if the following instruction is used:

using namespace KVImpactParameters;

Fitting a given inclusive P(X) distribution

First initialize the estimator with the required fitting function and kernel, such as for example:

--/ use 3rd order exponential polynomial function of Rogly et al with gamma kernel:
KVImpactParameters::bayesian_estimator<KVImpactParameters::rogly_fitting_function<3>,KVImpactParameters::gamma_kernel> ipd;
--/ or use algebraic function of Frankland et al with a binomial distribution kernel:
KVImpactParameters::bayesian_estimator<KVImpactParameters::algebraic_fitting_function, KVImpactParameters::BD_kernel> ipd;

See rogly_fitting_function, algebraic_fitting_function, gamma_kernel and NBD_kernel for more details.

Assumng a pointer TH1* h to a histogram containing the inclusive distribution for an observable filled from data, the first step is to transform the histogram into a correctly normalized probability distribution (taking bin widths into account):

ipd.RenormaliseHisto(h);

Then to begin the fitting process, call the method

ipd.FitHisto();

(if the histogram to fit was already correctly normalised, you can skip the first method and call this one giving the histogram pointer as argument). This will prepare initial parameter values for the fit based on the histogram data, then perform a first fit attempt. As this first attempt is never successful, you should then open the Fit Panel by right-clicking on the histogram in the canvas, and continue fitting using "Previous Fit", adjusting the range of the fit, and if necessary the parameter limits, until a satisfactory fit is achieved.

Using the results of the fit

Once a fit has been successful, the bayesian_estimator object can be used to deduce impact parameter distributions etc. for the fitted observable. This can be just after performing the fit as in the previous section (after first calling update_fit_params() - otherwise the internal fit parameter values are not necessarily consistent with the last performed fit), or using the already known parameters from a previous fit. In the latter case, you should initialize the object using the appropriate FittingFunction constructor, e.g. for algebraic_fitting_function which requires 5 parameters $\alpha,\gamma,\theta,X_{min},X_{max}$, you can initialise the estimator like so:

bayesian_estimator<algebraic_fitting_function, gamma_kernel> ipd({alpha,gamma,theta,Xmin,Xmax});

See the list of methods below which can then be used in order to exploit the fit result.

Definition at line 221 of file bayesian_estimator.h.

#include <bayesian_estimator.h>

Inheritance diagram for KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >:

Public Member Functions
	bayesian_estimator (Bool_t integer_variable=false)
	bayesian_estimator (const FittingFunction &previous_fit, Bool_t integer_variable=false)
virtual	~bayesian_estimator ()
void	DrawBDistForSelection (TH1 *sel, TH1 *incl, double &mean, double &sigma, Option_t *opt="", Color_t color=kRed, const TString &title="")
void	DrawBDistForSelectionFromIPHisto (TH1 *sel, TH1 *incl, double &mean, double &sigma, Option_t *opt="", Color_t color=kRed, const TString &title="")
double	DrawBDistForXSelection (KVValueRange< double > Xrange, Option_t *opt="", Color_t color=kRed, const TString &title="")
void	DrawCbDistForSelection (TH1 *sel, TH1 *incl, double &mean_cb, double &sigma_cb, Option_t *opt="", Color_t color=kRed, const TString &title="")
double	DrawCbDistForXSelection (double X1, double X2, Option_t *opt="", Color_t color=kRed, const TString &title="")
void	DrawFittedP_X (double norm=1.0, Option_t *opt="", Color_t color=kRed, const TString &title="")
void	DrawMeanXvsCb (const TString &title="", Color_t color=-1, Option_t *opt="")
void	DrawNormalisedMeanXvsb (const TString &title, Color_t color, Option_t *opt)
void	FitHisto (TH1 *h=nullptr)
TF1 &	GetB_dist_for_X_select ()
KVNameValueList	GetFitParameters () const
TF1 *	GetFittedP_X (double norm=1.0)
impact_parameter_distribution &	GetIPDist ()
TF2 *	GetJointProbabilityDistribution (KVValueRange< double > b_range, KVValueRange< double > X_range)
void	GetMeanAndSigmaBDistForSelection (TH1 *sel, TH1 *incl, double &mean, double &sigma)
void	GetMeanAndSigmaBDistForXSelection (KVValueRange< double > Xrange, double &mean, double &sigma)
TF1 &	GetMeanXvsCb ()
TGraph *	GraphBDistForXSelection (KVValueRange< double > Xrange, int npts=500)
TGraphErrors *	GraphMeanbvsX ()
TGraph *	GraphMeanXvsb (int npts=500)
TGraph *	GraphP_XForGivenB (double b, KVValueRange< double > Xrange, int npts=500)
void	Print (Option_t *="") const
void	RenormaliseHisto (TH1 *h)
void	SetIPDistFromHisto (TH1 *ip_histo)
void	SetIPDistParams (double sigmaR, double deltab)
TH2 *	TransformXaxisToBaxis (const TH2 *obs_vs_X, int baxis_nbins=100, double baxis_bmin=0, double baxis_bmax=1)
void	update_fit_params ()
Public Member Functions inherited from KVBase
	KVBase ()
	Default constructor. More...
	KVBase (const Char_t *name, const Char_t *title="")
	Ctor for object with given name and type. More...
	KVBase (const KVBase &)
	copy ctor More...
void	Clear (Option_t *opt="") override
	Clear object properties : name, type/title, number, label. More...
void	Copy (TObject &) const override
	Make a copy of this object. More...
const Char_t *	GetLabel () const
UInt_t	GetNumber () const
virtual TObject *	GetObject () const
virtual const Char_t *	GetType () const
Bool_t	HasLabel () const
virtual Bool_t	IsCalled (const Char_t *name) const
Bool_t	IsLabelled (const Char_t *l) const
virtual Bool_t	IsType (const Char_t *typ) const
virtual void	List ()
KVBase &	operator= (const KVBase &)
	copy assignment operator More...
void	Print (Option_t *option="") const override
Double_t	ProtectedGetX (const TF1 *func, Double_t val, int &status, Double_t xmin=0.0, Double_t xmax=0.0) const
void	SetLabel (const Char_t *lab)
virtual void	SetNumber (UInt_t num)
virtual void	SetType (const Char_t *str)

Private Member Functions
double	b_dist_for_arb_X_selection (double *x, double *p)
double	b_dist_for_arb_X_selection_from_histo (double *x, double *p)
double	b_dist_for_X_selection (double *x, double *p)
double	cb_dist_for_arb_X_selection (double *x, double *p)
double	cb_dist_for_X_selection (double *x, double *p)
double	cb_integrated_P_X (double *x, double *p)
double	mean_X_vs_b (double *x, double *par)
double	mean_X_vs_cb (double *x, double *par)
double	P_X_cb (double X, double cb)
double	P_X_cb_for_integral (double *x, double *par)
double	P_X_cb_for_TF2_obs_vs_b (double *x, double *)
double	P_X_cb_for_X_integral (double *x, double *par)
double	P_X_cb_for_X_integral_with_selection (double *x, double *par)
double	P_X_from_fit (double *x, double *par)

Private Attributes
TF1	B_dist_for_arb_X_select
TF1	B_dist_for_arb_X_select_from_histo
TF1	B_dist_for_X_select
TF1	Cb_dist_for_arb_X_select
TF1	Cb_dist_for_X_select
Bool_t	fIntegerVariable
impact_parameter_distribution	fIPDist
TF1	fitted_P_X
TH1 *	h_selection
TH1 *	histo
TF1	mean_X_vs_b_function
TF1	mean_X_vs_cb_function
TF1	p_X_cb_integrator
TF1	P_X_fit_function
TF1	p_X_X_integrator
TF1	p_X_X_integrator_with_selection
std::vector< double >	sel_rapp
FittingFunction	theFitter
FluctuationKernel	theKernel

Additional Inherited Members
Public Types inherited from KVBase
enum	EKaliVedaBits { kIsKaliVedaObject = BIT(23) }
Static Public Member Functions inherited from KVBase
static Bool_t	AreEqual (Double_t x, Double_t y, Long64_t maxdif=1)
	Comparison between two 64-bit floating-point values. More...
static void	BackupFileWithDate (const Char_t *path)
static void	CombineFiles (const Char_t *file1, const Char_t *file2, const Char_t *newfilename, Bool_t keep=kTRUE)
static void	Deprecated (const char *method, const char *advice)
static Bool_t	FindClassSourceFiles (const KVString &class_name, KVString &imp_file, KVString &dec_file, const KVString &dir_name=".")
static Bool_t	FindExecutable (TString &exec, const Char_t *path="$(PATH)")
static const Char_t *	FindFile (const Char_t *search, TString &wfil)
static const Char_t *	GetBINDIRFilePath (const Char_t *namefile="")
static const Char_t *	GetDATABASEFilePath ()
static const Char_t *	GetDATADIRFilePath (const Char_t *namefile="")
static KVString	GetDataSetEnv (const KVString &dataset, const KVString &type, const char *defval)
template<typename ValType >
static ValType	GetDataSetEnv (const KVString &dataset, const KVString &type, const ValType &defval)
static const Char_t *	GetETCDIRFilePath (const Char_t *namefile="")
static const Char_t *	GetExampleFilePath (const Char_t *library, const Char_t *namefile)
	Return full path to example file for given library (="KVMultiDet", "BackTrack", etc.) More...
static const Char_t *	GetINCDIRFilePath (const Char_t *namefile="")
static const Char_t *	GetKVBuildDate ()
	Returns KaliVeda build date. More...
static const Char_t *	GetKVBuildDir ()
	Returns top-level directory used for build. More...
static const Char_t *	GetKVBuildTime ()
	Returns KaliVeda build time. More...
static const Char_t *	GetKVBuildType ()
	Returns KaliVeda build type (cmake build: Release, Debug, RelWithDebInfo, ...) More...
static const Char_t *	GetKVBuildUser ()
	Returns username of person who performed build. More...
static int	GetKVMajorVersion ()
static int	GetKVMinorVersion ()
static const Char_t *	GetKVSourceDir ()
	Returns top-level directory of source tree used for build. More...
static const Char_t *	GetKVVersion ()
	Returns KaliVeda version string. More...
static const Char_t *	GetLIBDIRFilePath (const Char_t *namefile="")
static const Char_t *	GetListOfPlugins (const Char_t *base)
static const Char_t *	GetListOfPluginURIs (const Char_t *base)
static const Char_t *	GetPluginURI (const Char_t *base, const Char_t *plugin)
static void	GetTempFileName (TString &base)
static const Char_t *	GetTEMPLATEDIRFilePath (const Char_t *namefile="")
static const Char_t *	GetWORKDIRFilePath (const Char_t *namefile="")
static const Char_t *	gitBranch ()
	Returns git branch of sources. More...
static const Char_t *	gitCommit ()
	Returns last git commit of sources. More...
static void	InitEnvironment ()
static bool	is_gnuinstall ()
static Bool_t	IsEnvInit ()
static Bool_t	IsThisAPlugin (const TString &uri, TString &base)
static TPluginHandler *	LoadPlugin (const Char_t *base, const Char_t *uri="0")
static Bool_t	OpenContextMenu (const char *method, TObject *obj, const char *alt_method_name="")
static void	OpenTempFile (TString &base, std::ofstream &fp)
static void	PrintSplashScreen ()
	Prints welcome message and infos on version etc. More...
static Bool_t	SearchAndOpenKVFile (const Char_t *name, KVSQLite::database &dbfile, const Char_t *kvsubdir="")
static Bool_t	SearchAndOpenKVFile (const Char_t *name, std::ifstream &file, const Char_t *kvsubdir="", KVLockfile *locks=0)
static Bool_t	SearchAndOpenKVFile (const Char_t *name, std::ofstream &file, const Char_t *kvsubdir="", KVLockfile *locks=0)
static Bool_t	SearchKVFile (const Char_t *name, TString &fullpath, const Char_t *kvsubdir="")
static const Char_t *	WorkingDirectory ()

Constructor & Destructor Documentation

bayesian_estimator() [1/2]

template<class FittingFunction , class FluctuationKernel >

KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::bayesian_estimator ( Bool_t  integer_variable = false )

inline

Initialise estimator for fitting the inclusive distribution of an observable.

Parameters

[in]

integer_variable

[default:false] set true if the observable to be fitted only takes integer values

Definition at line 427 of file bayesian_estimator.h.

bayesian_estimator() [2/2]

template<class FittingFunction , class FluctuationKernel >

KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::bayesian_estimator ( const FittingFunction &  previous_fit, Bool_t  integer_variable = false  )

inline

Initialise estimator with results of a previous fit.

Parameters

[in]	previous_fit	parameters of a previous fit
[in]	integer_variable	[default:false] set true if the observable to be fitted only takes integer values

Definition at line 453 of file bayesian_estimator.h.

~bayesian_estimator()

template<class FittingFunction , class FluctuationKernel >

virtual KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::~bayesian_estimator ( )

inlinevirtual

Definition at line 480 of file bayesian_estimator.h.

Member Function Documentation

b_dist_for_arb_X_selection()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::b_dist_for_arb_X_selection ( double *  x, double *  p  )

inlineprivate

Function implementing the calculation of the impact parameter distribution $P(b|\mathbb{S})$ for an arbitrary selection of events $\mathbb{S}$

$$P(b|\mathbb{S})=P(b)\frac{\int P(X|b)\frac{P(X|\mathbb{S})}{P(X)}\,\mathrm{d}X}{\int P(X|\mathbb{S})\,\mathrm{d}X}$$

Returns

value of $P(b|\mathbb{S})$ for impact parameter $b$

Parameters

[in]	x[0]	impact parameter $b$
[in]	p[0],p[1]	integration limits for $X$, $[X_1,X_2]$

Definition at line 393 of file bayesian_estimator.h.

b_dist_for_arb_X_selection_from_histo()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::b_dist_for_arb_X_selection_from_histo ( double *  x, double *  p  )

inlineprivate

Function implementing the calculation of the impact parameter distribution $P(b|\mathbb{S})$ for an arbitrary selection of events $\mathbb{S}$

$$P(b|\mathbb{S})=P(b)\frac{\int P(X|b)\frac{P(X|\mathbb{S})}{P(X)}\,\mathrm{d}X}{\int P(X|\mathbb{S})\,\mathrm{d}X}$$

Returns

value of $P(b|\mathbb{S})$ for impact parameter $b$

Parameters

[in]	x[0]	impact parameter $b$
[in]	p[0],p[1]	integration limits for $X$, $[X_1,X_2]$

Definition at line 408 of file bayesian_estimator.h.

b_dist_for_X_selection()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::b_dist_for_X_selection ( double *  x, double *  p  )

inlineprivate

Function implementing the calculation of the impact parameter distribution $P(b|X_{1}<X<X_{2})$ for events selected by cuts in $X$, $X_{1}<X<X_{2}$

$$P(b|X_{1}<X<X_{2})=\frac{P(b)}{c_{X_{1}}-c_{X_{2}}}\int_{X_{1}}^{X_{2}}P(X|b)\,\mathrm{d}X$$

Returns

value of $P(b|X_{1}<X<X_{2})$ for impact parameter $b$

Parameters

[in]	x[0]	impact parameter $b$
[in]	p[0],p[1]	$X_1$, $X_2$

Definition at line 377 of file bayesian_estimator.h.

cb_dist_for_arb_X_selection()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::cb_dist_for_arb_X_selection ( double *  x, double *  p  )

inlineprivate

Function implementing the calculation of the centrality distribution $P(c_b|\mathbb{S})$ for an arbitrary selection of events $\mathbb{S}$

$$P(c_b|\mathbb{S})=\frac{\int P(X|c_b)\frac{P(X|\mathbb{S})}{P(X)}\,\mathrm{d}X}{\int P(X|\mathbb{S})\,\mathrm{d}X}$$

Returns

value of $P(c_b|\mathbb{S})$ for centrality $c_b$

Parameters

[in]	x[0]	centrality $c_b$
[in]	p[0],p[1]	integration limits for $X$, $[X_1,X_2]$

num*=(1./histo->Integral("width"));

Definition at line 360 of file bayesian_estimator.h.

cb_dist_for_X_selection()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::cb_dist_for_X_selection ( double *  x, double *  p  )

inlineprivate

Function implementing the calculation of the centrality distribution $P(c_b|X_{1}<X<X_{2})$ for events selected by cuts in $X$, $X_{1}<X<X_{2}$

$$P(c_b|X_{1}<X<X_{2})=\frac{1}{c_{X_{1}}-c_{X_{2}}}\int_{X_{1}}^{X_{2}}P(X|c_b)\,\mathrm{d}X$$

Returns

value of $P(c_b|X_{1}<X<X_{2})$ for centrality $c_b$

Parameters

[in]	x[0]	centrality $c_b$
[in]	p[0],p[1]	$X_1$, $X_2$

Definition at line 342 of file bayesian_estimator.h.

cb_integrated_P_X()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::cb_integrated_P_X ( double *  x, double *  p  )

inlineprivate

Function used to fit experimental $P(X)$ distribution by integrating the distribution $P(X|c_b)$

$$P(X)=\int P(X|c_b)\,\mathrm{d}c_b$$

Returns

value of $P(X)$ at $X$ for current fit parameters

Parameters

[in]	x[0]	$X$
[in]	p[0],p[1],...,p[Npar-1]	parameters of fitting function

Definition at line 319 of file bayesian_estimator.h.

DrawBDistForSelection()

template<class FittingFunction , class FluctuationKernel >

void KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::DrawBDistForSelection ( TH1 *  sel, TH1 *  incl, double &  mean, double &  sigma, Option_t *  opt = "", Color_t  color = kRed, const TString &  title = ""  )

inline

Draw impact parameter distribution (as differential cross-section) for an arbitrary selection $\mathbb{S}$ of data,

$$\frac{\mathrm{d}\sigma}{\mathrm{d}b}=\sigma_{\mathrm{tot}}P(b|\mathbb{S})=P(b)\frac{\int P(X|b)\frac{P(X|\mathbb{S})}{P(X)}\,\mathrm{d}X}{\int P(X|\mathbb{S})\,\mathrm{d}X}$$

Parameters

[in]	sel	pointer to histogram containing observable distribution for selected events
[in]	incl	pointer to histogram containing inclusive observable distribution
[out]	mean	mean value of b distribution
[out]	sigma	standard deviation of b distribution
[in]	opt	drawing option if required, e.g. "same"
[in]	color	colour to use for drawing distribution
[in]	title	title to affect to the drawn distribution

Note

Histograms sel and incl must have exactly the same axis definitions, binning etc.

To have absolute impact parameters in [fm], call SetIPDistParams() first with the total measured cross-section $\sigma_R$ in [mb] and the desired fall-off parameter $\Delta b$ in [fm] (see impact_parameter_distribution).

Definition at line 847 of file bayesian_estimator.h.

DrawBDistForSelectionFromIPHisto()

template<class FittingFunction , class FluctuationKernel >

void KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::DrawBDistForSelectionFromIPHisto ( TH1 *  sel, TH1 *  incl, double &  mean, double &  sigma, Option_t *  opt = "", Color_t  color = kRed, const TString &  title = ""  )

inline

Draw impact parameter distribution (as differential cross-section) for an arbitrary selection $\mathbb{S}$ of data,

$$\frac{\mathrm{d}\sigma}{\mathrm{d}b}=\sigma_{\mathrm{tot}}P(b|\mathbb{S})=P(b)\frac{\int P(X|b)\frac{P(X|\mathbb{S})}{P(X)}\,\mathrm{d}X}{\int P(X|\mathbb{S})\,\mathrm{d}X}$$

Parameters

[in]	sel	pointer to histogram containing observable distribution for selected events
[in]	incl	pointer to histogram containing inclusive observable distribution
[out]	mean	mean value of b distribution
[out]	sigma	standard deviation of b distribution
[in]	opt	drawing option if required, e.g. "same"
[in]	color	colour to use for drawing distribution
[in]	title	title to affect to the drawn distribution

Note

Histograms sel and incl must have exactly the same axis definitions, binning etc.

call SetIPDistFromHisto() first to set the impact parameter distribution (see impact_parameter_distribution).

Definition at line 914 of file bayesian_estimator.h.

DrawBDistForXSelection()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::DrawBDistForXSelection ( KVValueRange< double >  Xrange, Option_t *  opt = "", Color_t  color = kRed, const TString &  title = ""  )

inline

Draw impact parameter distribution (as differential cross-section) for observable cuts $X_1<X<X_2$

$$\frac{\mathrm{d}\sigma}{\mathrm{d}b}=\sigma_{\mathrm{tot}}P(b|X_{1}<X<X_{2})=\frac{P(b)}{c_{X_{1}}-c_{X_{2}}}\int_{X_{1}}^{X_{2}}P(X|b)\,\mathrm{d}X$$

Parameters

[in]	X1	lower limit for observable cut
[in]	X2	upper limit for observable cut
[in]	opt	drawing option if required, e.g. "same"
[in]	color	colour to use for drawing distribution
[in]	title	title to affect to the drawn distribution

Returns

maximum value of differential cross-section

Note

To have absolute impact parameters in [fm], call SetIPDistParams() first with the total measured cross-section $\sigma_R$ in [mb] and the desired fall-off parameter $\Delta b$ in [fm] (see impact_parameter_distribution).

Definition at line 781 of file bayesian_estimator.h.

DrawCbDistForSelection()

template<class FittingFunction , class FluctuationKernel >

void KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::DrawCbDistForSelection ( TH1 *  sel, TH1 *  incl, double &  mean_cb, double &  sigma_cb, Option_t *  opt = "", Color_t  color = kRed, const TString &  title = ""  )

inline

Draw centrality distribution for an arbitrary selection $\mathbb{S}$ of data,

$$P(c_b|\mathbb{S})=\frac{\int P(X|c_b)\frac{P(X|\mathbb{S})}{P(X)}\,\mathrm{d}X}{\int P(X|\mathbb{S})\,\mathrm{d}X}$$

Parameters

[in]	sel	pointer to histogram containing observable distribution for selected events
[in]	incl	pointer to histogram containing inclusive observable distribution
[out]	mean_cb	mean value of c_b distribution
[out]	sigma_cb	standard deviation of c_b distribution
[in]	opt	drawing option if required, e.g. "same"
[in]	color	colour to use for drawing distribution
[in]	title	title to affect to the drawn distribution

Note

Histograms sel and incl must have exactly the same axis definitions, binning etc.

• extract first and last (not empty) bins -
• define the P(X|S)/P(X) vector (used for integrand) -
• set parameters -
• fill the graph -
• compute the standard deviation -
• draw and options -

Definition at line 710 of file bayesian_estimator.h.

DrawCbDistForXSelection()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::DrawCbDistForXSelection ( double  X1, double  X2, Option_t *  opt = "", Color_t  color = kRed, const TString &  title = ""  )

inline

Draw centrality distribution for observable cuts $X_1<X<X_2$

$$P(c_b|X_{1}<X<X_{2})=\frac{1}{c_{X_{1}}-c_{X_{2}}}\int_{X_{1}}^{X_{2}}P(X|c_b)\,\mathrm{d}X$$

Parameters

[in]	X1	lower limit for observable cut
[in]	X2	upper limit for observable cut
[in]	opt	drawing option if required, e.g. "same"
[in]	color	colour to use for drawing distribution
[in]	title	title to affect to the drawn distribution

Returns

maximum value of probability distribution

Definition at line 687 of file bayesian_estimator.h.

DrawFittedP_X()

template<class FittingFunction , class FluctuationKernel >

void KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::DrawFittedP_X ( double  norm = 1.0, Option_t *  opt = "", Color_t  color = kRed, const TString &  title = ""  )

inline

Draw the distribution $P(X)$ resulting from the fit to the experimental distribution

Parameters

[in]	norm	optional normalisation parameter e.g. if differential cross-section required: norm= $\sigma_R$
[in]	opt	drawing option if required, e.g. "same"
[in]	color	colour to use for drawing distribution
[in]	title	title to affect to the drawn distribution

Definition at line 1058 of file bayesian_estimator.h.

DrawMeanXvsCb()

template<class FittingFunction , class FluctuationKernel >

void KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::DrawMeanXvsCb ( const TString &  title = "", Color_t  color = -1, Option_t *  opt = ""  )

inline

Draw the dependence of the mean value of the observable with centrality, $\bar{X}(c_b)$, given by

$$\bar{X}(c_b)=\theta k(c_b)$$

Parameters

[in]	title	title to affect to the drawn function
[in]	color	colour to use for drawing function
[in]	opt	drawing option if required, e.g. "same"

Definition at line 567 of file bayesian_estimator.h.

DrawNormalisedMeanXvsb()

template<class FittingFunction , class FluctuationKernel >

void KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::DrawNormalisedMeanXvsb ( const TString &  title, Color_t  color, Option_t *  opt  )

inline

Draw the dependence of the mean value of the observable with impact parameter, $\bar{X}(b)$, given by

$$\bar{X}(b)=\theta k(b)$$

but with $\bar{X}$ normalised so that $X_{\mathrm{min}}=0$ and $X_{\mathrm{max}}=1$, allowing to compare shapes for different fits

Parameters

[in]	title	title to affect to the drawn function
[in]	color	colour to use for drawing function
[in]	opt	drawing option if required, e.g. "same"

Note

To have absolute impact parameters in [fm], call SetIPDistParams() first with the total measured cross-section $\sigma_R$ in [mb] and the desired fall-off parameter $\Delta b$ in [fm] (see impact_parameter_distribution).

Definition at line 1104 of file bayesian_estimator.h.

FitHisto()

template<class FittingFunction , class FluctuationKernel >

void KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::FitHisto ( TH1 *  h = nullptr )

inline

Method used to fit a data histogram of $P(X)$ in order to deduce the parameters of $P(X|b)$.

Prepare initial parameter values for fit based on data in histogram, then perform a first fit attempt. As this first attempt is never successful, you should then open the Fit Panel by right-clicking on the histogram in the canvas, and continue fitting using "Previous Fit", adjusting the range of the fit, and if necessary the parameter limits, until a satisfactory fit is achieved.

Note

Call RenormaliseHisto() first if histo is not a correctly normalised probability distribution

Parameters

[in]

h

pointer to histogram to fit. if not given, use internal histogram set by previous call to RenormaliseHisto()

Definition at line 494 of file bayesian_estimator.h.

GetB_dist_for_X_select()

template<class FittingFunction , class FluctuationKernel >

TF1& KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::GetB_dist_for_X_select ( )

inline

Definition at line 817 of file bayesian_estimator.h.

GetFitParameters()

template<class FittingFunction , class FluctuationKernel >

KVNameValueList KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::GetFitParameters ( ) const

inline

Returns list of fit parameters as named values

Definition at line 1099 of file bayesian_estimator.h.

GetFittedP_X()

template<class FittingFunction , class FluctuationKernel >

TF1* KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::GetFittedP_X ( double  norm = 1.0 )

inline

Access the distribution $P(X)$ resulting from the fit to the experimental distribution

Parameters

[in]

norm

optional normalisation parameter e.g. if differential cross-section required: norm= $\sigma_R$

Returns

pointer to TF1 function object

Definition at line 1073 of file bayesian_estimator.h.

GetIPDist()

template<class FittingFunction , class FluctuationKernel >

impact_parameter_distribution& KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::GetIPDist ( )

inline

Access the impact parameter distribution assumed to correspond to the full inclusive distribution of $X$, $P(X)$.

Returns

reference to impact_parameter_distribution object

See also

impact_parameter_distribution

Definition at line 556 of file bayesian_estimator.h.

GetJointProbabilityDistribution()

template<class FittingFunction , class FluctuationKernel >

TF2* KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::GetJointProbabilityDistribution ( KVValueRange< double >  b_range, KVValueRange< double >  X_range  )

inline

Create and return a 2D function representing the joint probability $P(X,b)$ with $b$ on the abscissa and the observable on the ordinate

Definition at line 1135 of file bayesian_estimator.h.

GetMeanAndSigmaBDistForSelection()

template<class FittingFunction , class FluctuationKernel >

void KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::GetMeanAndSigmaBDistForSelection ( TH1 *  sel, TH1 *  incl, double &  mean, double &  sigma  )

inline

Calculate mean and standard deviation of impact parameter distribution for an arbitrary selection $\mathbb{S}$ of data

$$P(b|\mathbb{S})=P(b)\frac{\int P(X|b)\frac{P(X|\mathbb{S})}{P(X)}\,\mathrm{d}X}{\int P(X|\mathbb{S})\,\mathrm{d}X}$$

Parameters

[in]	sel	pointer to histogram containing observable distribution for selected events
[in]	incl	pointer to histogram containing inclusive observable distribution
[out]	mean	mean value of impact parameter for selection, $\langle b\rangle$
[out]	sigma	standard deviation of impact parameter distribution

Note

Histograms sel and incl must have exactly the same axis definitions, binning etc.

To have absolute impact parameters in [fm], call SetIPDistParams() first with the total measured cross-section $\sigma_R$ in [mb] and the desired fall-off parameter $\Delta b$ in [fm] (see impact_parameter_distribution).

Definition at line 978 of file bayesian_estimator.h.

GetMeanAndSigmaBDistForXSelection()

template<class FittingFunction , class FluctuationKernel >

void KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::GetMeanAndSigmaBDistForXSelection ( KVValueRange< double >  Xrange, double &  mean, double &  sigma  )

inline

Calculate mean and standard deviation of impact parameter distribution for observable cuts $X_1<X<X_2$

$$P(b|X_{1}<X<X_{2})=\frac{P(b)}{c_{X_{1}}-c_{X_{2}}}\int_{X_{1}}^{X_{2}}P(X|b)\,\mathrm{d}X$$

Parameters

[in]	X1	lower limit for observable cut
[in]	X2	upper limit for observable cut
[out]	mean	mean value of impact parameter for selection, $\langle b\rangle$
[out]	sigma	standard deviation of impact parameter distribution

Note

To have absolute impact parameters in [fm], call SetIPDistParams() first with the total measured cross-section $\sigma_R$ in [mb] and the desired fall-off parameter $\Delta b$ in [fm] (see impact_parameter_distribution).

Definition at line 1023 of file bayesian_estimator.h.

GetMeanXvsCb()

template<class FittingFunction , class FluctuationKernel >

TF1& KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::GetMeanXvsCb ( )

inline

Access the function implementing the dependence of the mean value of the observable with centrality, $\bar{X}(c_b)$, given by

$$\bar{X}(c_b)=\theta k(c_b)$$

Returns

reference to TF1 function object

Definition at line 580 of file bayesian_estimator.h.

GraphBDistForXSelection()

template<class FittingFunction , class FluctuationKernel >

TGraph* KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::GraphBDistForXSelection ( KVValueRange< double >  Xrange, int  npts = 500  )

inline

Graph impact parameter distribution (as differential cross-section) for observable cuts $X_1<X<X_2$

$$\frac{\mathrm{d}\sigma}{\mathrm{d}b}=\sigma_{\mathrm{tot}}P(b|X_{1}<X<X_{2})=\frac{P(b)}{c_{X_{1}}-c_{X_{2}}}\int_{X_{1}}^{X_{2}}P(X|b)\,\mathrm{d}X$$

Parameters

[in]

Xrange

range of X for observable cut

Returns

graph of differential cross-section

Note

To have absolute impact parameters in [fm], call SetIPDistParams() first with the total measured cross-section $\sigma_R$ in [mb] and the desired fall-off parameter $\Delta b$ in [fm] (see impact_parameter_distribution).

Definition at line 821 of file bayesian_estimator.h.

GraphMeanbvsX()

template<class FittingFunction , class FluctuationKernel >

TGraphErrors* KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::GraphMeanbvsX ( )

inline

Produce a graph of mean impact parameter vs. X

Definition at line 642 of file bayesian_estimator.h.

GraphMeanXvsb()

template<class FittingFunction , class FluctuationKernel >

TGraph* KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::GraphMeanXvsb ( int  npts = 500 )

inline

Create a graph of the dependence of the mean value of the observable with impact parameter, $\bar{X}(b)$, given by

$$\bar{X}(b)=\theta k(b)$$

Note

To have absolute impact parameters in [fm], call SetIPDistParams() first with the total measured cross-section $\sigma_R$ in [mb] and the desired fall-off parameter $\Delta b$ in [fm] (see impact_parameter_distribution).

Definition at line 594 of file bayesian_estimator.h.

GraphP_XForGivenB()

template<class FittingFunction , class FluctuationKernel >

TGraph* KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::GraphP_XForGivenB ( double  b, KVValueRange< double >  Xrange, int  npts = 500  )

inline

Draw conditional probability distribution of observable, $P(X|b)$, for a single value of $b$.

Parameters

[in]	b	impact parameter
[in]	Xrange	range of values of observable for graph
[in]	npts	number of points used in graph

Definition at line 1082 of file bayesian_estimator.h.

mean_X_vs_b()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::mean_X_vs_b ( double *  x, double *  par  )

inlineprivate

Function used to fit/draw dependence of mean observable on impact parameter, $\bar{X}(b)$

Parameters

[in]	x[0]	impact parameter $b$
[in]	p[0],p[1],...,p[Npar-1]	parameters of fitting function

Returns

mean value of $X$ for given centrality

Definition at line 256 of file bayesian_estimator.h.

mean_X_vs_cb()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::mean_X_vs_cb ( double *  x, double *  par  )

inlineprivate

Function used to fit/draw dependence of mean observable on centrality, $\bar{X}(c_b)$

Parameters

[in]	x[0]	centrality $c_b$
[in]	p[0],p[1],...,p[Npar-1]	parameters of fitting function

Returns

mean value of $X$ for given centrality

Definition at line 246 of file bayesian_estimator.h.

P_X_cb()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::P_X_cb ( double  X, double  cb  )

inlineprivate

Returns

probability of observable $X$ for centrality $c_b$, using FluctuationKernel

Parameters

[in]	X	the value of the observable $X$
[in]	cb	the centrality $c_b$

Definition at line 266 of file bayesian_estimator.h.

P_X_cb_for_integral()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::P_X_cb_for_integral ( double *  x, double *  par  )

inlineprivate

Function used for the integrand of

$$P(X)=\int P(X|c_b)\,\mathrm{d}c_b$$

Parameters

[in]	x[0]	centrality $c_b$
[in]	par[0]	observable value, $X$

Definition at line 284 of file bayesian_estimator.h.

P_X_cb_for_TF2_obs_vs_b()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::P_X_cb_for_TF2_obs_vs_b ( double *  x, double *    )

inlineprivate

Returns

conditional probability distribution $P(X|b)$, X is ordinate, b is abscissa

Parameters

[in]	x[0]	impact parameter b
[in]	x[1]	value of observable X

Definition at line 274 of file bayesian_estimator.h.

P_X_cb_for_X_integral()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::P_X_cb_for_X_integral ( double *  x, double *  par  )

inlineprivate

Function used for the integrand of

$$\int P(X|c_b)\,\mathrm{d}X$$

used to calculate centrality distributions for data.

Parameters

[in]	x[0]	observable $X$
[in]	par[0]	centrality value $c_b$

Definition at line 294 of file bayesian_estimator.h.

P_X_cb_for_X_integral_with_selection()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::P_X_cb_for_X_integral_with_selection ( double *  x, double *  par  )

inlineprivate

Function used for the integrand of

$$\int P(X|c_b)\frac{P(X|\mathbb{S})}{P(X)}\,\mathrm{d}X$$

used to calculate centrality distributions for data selection $\mathbb{S}$

Parameters

[in]	x[0]	observable $X$
[in]	par[0]	centrality value $c_b$

Definition at line 305 of file bayesian_estimator.h.

P_X_from_fit()

template<class FittingFunction , class FluctuationKernel >

double KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::P_X_from_fit ( double *  x, double *  par  )

inlineprivate

Same as cb_integrated_P_X(), but just using current values of parameters. Used to display fit result.

Parameters

[in]	x[0]	$X$
[in]	par[0]	normalisation factor

Returns

value of $P(X)$ at $X$ for current fit parameters

Definition at line 333 of file bayesian_estimator.h.

Print()

template<class FittingFunction , class FluctuationKernel >

void KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::Print ( Option_t *  = "" ) const

inline

Print informations on current values of fit parameters

Definition at line 1094 of file bayesian_estimator.h.

RenormaliseHisto()

template<class FittingFunction , class FluctuationKernel >

void KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::RenormaliseHisto ( TH1 *  h )

inline

Turn data histogram for observable into probability distribution $P(X)$ (taking account of binning).

After calling this method, the histogram fitting procedure can be started by calling FitHisto().

Parameters

[in]

h

pointer to histogram to normalise

Definition at line 482 of file bayesian_estimator.h.

SetIPDistFromHisto()

template<class FittingFunction , class FluctuationKernel >

void KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::SetIPDistFromHisto ( TH1 *  ip_histo )

inline

Any distributions of $b$ deduced from data depend on the impact parameter distribution $P(b)$ which is assumed for the full inclusive dataset, i.e. for all collisions contributing to the $P(X)$ distribution fitted in order to deduce the parameters for $k(c_b)$ and $\theta$.

By default this is a triangular distribution between $b=0$ & $b=1$ fm with cross-section 31.4 mb, which can be treated as though it were the sharp cut-off distribution for $\hat{b}=b/b_{\mathrm{max}}$.

Todo:

The differential cross-section in this case is incorrect, although mean values and variaces are calculated correctly

To obtain absolute impact parameters, call this method with

Parameters

[in]

ip_histo

the impact parameter distribution in [mb]

Definition at line 537 of file bayesian_estimator.h.

SetIPDistParams()

template<class FittingFunction , class FluctuationKernel >

void KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::SetIPDistParams ( double  sigmaR, double  deltab  )

inline

Any distributions of $b$ deduced from data depend on the impact parameter distribution $P(b)$ which is assumed for the full inclusive dataset, i.e. for all collisions contributing to the $P(X)$ distribution fitted in order to deduce the parameters for $k(c_b)$ and $\theta$.

By default this is a triangular distribution between $b=0$ & $b=1$ fm with cross-section 31.4 mb, which can be treated as though it were the sharp cut-off distribution for $\hat{b}=b/b_{\mathrm{max}}$.

Todo:

The differential cross-section in this case is incorrect, although mean values and variaces are calculated correctly

To obtain absolute impact parameters, call this method with

Parameters

[in]	sigmaR	total reaction cross-section $\sigma_R$ in [mb]
[in]	deltab	fall-off parameter for distribution $\Delta b$ in [fm]

See also

impact_parameter_distribution

Definition at line 515 of file bayesian_estimator.h.

TransformXaxisToBaxis()

template<class FittingFunction , class FluctuationKernel >

TH2* KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::TransformXaxisToBaxis ( const TH2 *  obs_vs_X, int  baxis_nbins = 100, double  baxis_bmin = 0, double  baxis_bmax = 1  )

inline

Take a 2D histogram of some observable as a function of X. Generate a new 2D histogram of the observable's dependence on b.

From an original idea by Caterina Ciampi.

Definition at line 614 of file bayesian_estimator.h.

update_fit_params()

template<class FittingFunction , class FluctuationKernel >

void KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::update_fit_params ( )

inline

Retrieve latest values of fit parameters from fitting function stored with histogram, in case the internal parameters do not correspond to them.

Note

This method may be obsolete, the problem doesn't seem to occur anymore

Definition at line 669 of file bayesian_estimator.h.

Member Data Documentation

B_dist_for_arb_X_select

template<class FittingFunction , class FluctuationKernel >

TF1 KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::B_dist_for_arb_X_select

private

Definition at line 239 of file bayesian_estimator.h.

B_dist_for_arb_X_select_from_histo

template<class FittingFunction , class FluctuationKernel >

TF1 KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::B_dist_for_arb_X_select_from_histo

private

Definition at line 240 of file bayesian_estimator.h.

B_dist_for_X_select

template<class FittingFunction , class FluctuationKernel >

TF1 KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::B_dist_for_X_select

private

Definition at line 238 of file bayesian_estimator.h.

Cb_dist_for_arb_X_select

template<class FittingFunction , class FluctuationKernel >

TF1 KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::Cb_dist_for_arb_X_select

private

Definition at line 237 of file bayesian_estimator.h.

Cb_dist_for_X_select

template<class FittingFunction , class FluctuationKernel >

TF1 KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::Cb_dist_for_X_select

private

Definition at line 236 of file bayesian_estimator.h.

fIntegerVariable

template<class FittingFunction , class FluctuationKernel >

Bool_t KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::fIntegerVariable

private

Definition at line 242 of file bayesian_estimator.h.

fIPDist

template<class FittingFunction , class FluctuationKernel >

impact_parameter_distribution KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::fIPDist

private

Definition at line 244 of file bayesian_estimator.h.

fitted_P_X

template<class FittingFunction , class FluctuationKernel >

TF1 KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::fitted_P_X

private

Definition at line 235 of file bayesian_estimator.h.

h_selection

template<class FittingFunction , class FluctuationKernel >

TH1* KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::h_selection

private

Definition at line 227 of file bayesian_estimator.h.

histo

template<class FittingFunction , class FluctuationKernel >

TH1* KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::histo

private

Definition at line 226 of file bayesian_estimator.h.

mean_X_vs_b_function

template<class FittingFunction , class FluctuationKernel >

TF1 KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::mean_X_vs_b_function

private

Definition at line 232 of file bayesian_estimator.h.

mean_X_vs_cb_function

template<class FittingFunction , class FluctuationKernel >

TF1 KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::mean_X_vs_cb_function

private

Definition at line 231 of file bayesian_estimator.h.

p_X_cb_integrator

template<class FittingFunction , class FluctuationKernel >

TF1 KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::p_X_cb_integrator

private

Definition at line 229 of file bayesian_estimator.h.

P_X_fit_function

template<class FittingFunction , class FluctuationKernel >

TF1 KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::P_X_fit_function

private

Definition at line 230 of file bayesian_estimator.h.

p_X_X_integrator

template<class FittingFunction , class FluctuationKernel >

TF1 KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::p_X_X_integrator

private

Definition at line 233 of file bayesian_estimator.h.

p_X_X_integrator_with_selection

template<class FittingFunction , class FluctuationKernel >

TF1 KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::p_X_X_integrator_with_selection

private

Definition at line 234 of file bayesian_estimator.h.

sel_rapp

template<class FittingFunction , class FluctuationKernel >

std::vector<double> KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::sel_rapp

private

Definition at line 228 of file bayesian_estimator.h.

theFitter

template<class FittingFunction , class FluctuationKernel >

FittingFunction KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::theFitter

private

Definition at line 223 of file bayesian_estimator.h.

theKernel

template<class FittingFunction , class FluctuationKernel >

FluctuationKernel KVImpactParameters::bayesian_estimator< FittingFunction, FluctuationKernel >::theKernel

private

Definition at line 224 of file bayesian_estimator.h.