#include "Headers/Modelling.h"

Inheritance diagram for cbl::modelling::Modelling:

[legend]

Public Member Functions
void	m_set_posterior (const int seed)
	set the interal variable m_posterior More...

Constructors/destructors
	Modelling ()=default
	default constuctor

virtual	~Modelling ()=default
	default destructor

Member functions used to get the protected members
std::shared_ptr< data::Data >	data ()
	return the dataset More...

std::shared_ptr< data::Data >	data_fit ()
	return the dataset More...

std::shared_ptr< statistics::Likelihood >	likelihood ()
	return the likelihood parameters More...

std::shared_ptr< statistics::Posterior >	posterior ()
	return the posterior parameters More...

std::shared_ptr< statistics::ModelParameters >	likelihood_parameters ()
	return the likelihood parameters More...

std::shared_ptr< statistics::ModelParameters >	posterior_parameters ()
	return the posterior parameters More...

virtual void	set_parameter_from_string (const std::string parameter, const double value)
	set the value of a parameter providing its name string More...

virtual double	get_parameter_from_string (const std::string parameter) const
	get the value of a parameter providing its name string More...

std::shared_ptr< statistics::PriorDistribution >	get_prior (const int i)
	get the internal variable m_parameter_priors More...

std::shared_ptr< statistics::Model >	get_response_function ()
	return the response function used to compute the super-sample covariance More...

Member functions used to set internal parameters
void	reset_fit_range ()
	reset the fit range More...

void	set_fit_range (const double xmin, const double xmax)
	set the fit range More...

void	set_fit_range (const double xmin, const double xmax, const double ymin, const double ymax)
	set the fit range More...

void	set_data (const std::shared_ptr< data::Data > dataset)
	set the dataset More...

void	set_likelihood (const statistics::LikelihoodType likelihood_type, const std::vector< size_t > x_index={0, 2}, const int w_index=-1, const double prec=1.e-10, const int Nres=-1)
	set the likelihood function More...

void	set_likelihood (const cbl::statistics::Likelihood_function log_likelihood_function)
	set the likelihood function, given a user-defined log-likelihood function More...

Member functions used to manage likelihood/posterior
distributions
void	maximize_likelihood (const std::vector< double > start, const std::vector< std::vector< double >> parameter_limits, const unsigned int max_iter=10000, const double tol=1.e-6, const double epsilon=1.e-3)
	function that maximizes the posterior, finds the best-fit parameters and stores them in the model More...

void	maximize_posterior (const std::vector< double > start, const unsigned int max_iter=10000, const double tol=1.e-6, const double epsilon=1.e-3, const int seed=666)
	function that maximizes the posterior, finds the best-fit parameters and stores them in the model More...

void	sample_posterior (const int chain_size, const int nwalkers, const int seed=666, const double aa=2, const bool parallel=true)
	sample the posterior, initializing the chains by drawing from the prior distributions More...

void	sample_posterior (const int chain_size, const int nwalkers, const double radius, const std::vector< double > start, const unsigned int max_iter=10000, const double tol=1.e-6, const double epsilon=1.e-3, const int seed=666, const double aa=2, const bool parallel=true)
	sample the posterior, initializing the chains in a ball around the posterior best-fit parameters values More...

void	sample_posterior (const int chain_size, const int nwalkers, std::vector< double > &value, const double radius, const int seed=666, const double aa=2, const bool parallel=true)
	sample the posterior, initializing the chains by drawing from the prior distributions More...

void	sample_posterior (const int chain_size, const std::vector< std::vector< double >> chain_value, const int seed=666, const double aa=2, const bool parallel=true)
	sample the posterior, initializing the chains with input values More...

void	sample_posterior (const int chain_size, const int nwalkers, const std::string input_dir, const std::string input_file, const int seed=666, const double aa=2, const bool parallel=true)
	sample the posterior, initializing the chains reading the input values from an input file More...

void	importance_sampling (const std::string input_dir, const std::string input_file, const int seed=666, const std::vector< size_t > column={}, const int header_lines_to_skip=1, const bool is_FITS_format=false, const bool apply_to_likelihood=false)
	perform importance sampling More...

Member functions used for Input/Output
void	write_chain (const std::string output_dir, const std::string output_file, const int start=0, const int thin=1, const bool is_FITS_format=false, const int prec=5, const int ww=14)
	write the chains obtained after the MCMC sampling More...

void	read_chain (const std::string input_dir, const std::string input_file, const int nwalkers, const std::vector< size_t > columns={}, const int skip_header=1, const bool fits=false)
	read the chains More...

void	show_results (const int start=0, const int thin=1, const int nbins=50, const bool show_mode=false, const int ns=-1)
	show the results of the MCMC sampling on screen More...

void	write_results (const std::string output_dir, const std::string root_file, const int start=0, const int thin=1, const int nbins=50, const bool fits=false, const bool compute_mode=false, const int ns=-1)
	write the results of the MCMC sampling to file More...

virtual void	write_model (const std::string output_dir, const std::string output_file, const std::vector< double > xx, const std::vector< double > parameters)
	write the model at xx for given parameters More...

virtual void	write_model (const std::string output_dir, const std::string output_file, const std::vector< double > xx, const std::vector< double > yy, const std::vector< double > parameters)
	write the model at xx, yy for given parameters More...

virtual void	write_model_at_bestfit (const std::string output_dir, const std::string output_file, const std::vector< double > xx)
	write the model at xx with best-fit parameters obtained from posterior maximization More...

virtual void	write_model_at_bestfit (const std::string output_dir, const std::string output_file, const std::vector< double > xx, const std::vector< double > yy)
	write the model at xx, yy with best-fit parameters obtained from likelihood maximization More...

virtual void	write_model_from_chains (const std::string output_dir, const std::string output_file, const std::vector< double > xx, const int start=0, const int thin=1)
	write the model at xx computing 16th, 50th and 84th percentiles from the chains More...

virtual void	write_model_from_chains (const std::string output_dir, const std::string output_file, const std::vector< double > xx, const std::vector< double > yy, const int start=0, const int thin=1)
	write the model at xx, yy computing 16th, 50th and 84th percentiles from the chains More...

double	reduced_chi2 (const std::vector< double > parameter={})
	the reduced \(\chi^2\) More...

Protected Member Functions
void	m_set_prior (std::vector< statistics::PriorDistribution > prior_distribution)
	set the internal variable m_parameter_priors More...

void	m_isSet_response ()
	check if the response function used to compute the super-sample covariance is set

Protected Attributes
std::shared_ptr< data::Data >	m_data = NULL
	input data to be modelled

bool	m_fit_range = false
	check if fit range has been set

std::shared_ptr< data::Data >	m_data_fit
	input data restricted to the range used for the fit

std::shared_ptr< statistics::Model >	m_model = NULL
	input model

std::shared_ptr< statistics::Model >	m_response_func = NULL
	response function for the computation of the super-sample covariance

std::shared_ptr< statistics::Likelihood >	m_likelihood = NULL
	likelihood

std::vector< std::shared_ptr< statistics::PriorDistribution > >	m_parameter_priors
	prior

std::shared_ptr< statistics::Posterior >	m_posterior = NULL
	posterior

Detailed Description

The class Modelling.

This file defines the interface of the base class Modelling, used for modelling any kind of measurements

Definition at line 64 of file Modelling.h.

Member Function Documentation

◆ data()

std::shared_ptr<data::Data> cbl::modelling::Modelling::data ( )

inline

return the dataset

Returns: pointer to the current dataset

Definition at line 141 of file Modelling.h.

◆ data_fit()

std::shared_ptr<data::Data> cbl::modelling::Modelling::data_fit ( )

inline

return the dataset

Returns: pointer to the current dataset

Definition at line 147 of file Modelling.h.

◆ get_parameter_from_string()

virtual double cbl::modelling::Modelling::get_parameter_from_string ( const std::string parameter ) const

inlinevirtual

get the value of a parameter providing its name string

Parameters

parameter parameter name to get

Returns: the parameter value

Definition at line 196 of file Modelling.h.

◆ get_prior()

std::shared_ptr<statistics::PriorDistribution> cbl::modelling::Modelling::get_prior ( const int i )

inline

get the internal variable m_parameter_priors

Parameters

i	prior index

Returns: i-th prior distribution

Definition at line 206 of file Modelling.h.

◆ get_response_function()

std::shared_ptr<statistics::Model> cbl::modelling::Modelling::get_response_function ( )

inline

return the response function used to compute the super-sample covariance

Returns: pointer to the response function

Definition at line 214 of file Modelling.h.

◆ importance_sampling()

void cbl::modelling::Modelling::importance_sampling	(	const std::string	input_dir,
		const std::string	input_file,
		const int	seed = `666`,
		const std::vector< size_t >	column = `{}`,
		const int	header_lines_to_skip = `1`,
		const bool	is_FITS_format = `false`,
		const bool	apply_to_likelihood = `false`
	)

perform importance sampling

Importance sampling is a convenient technique to join independet datasets.

This function takes in input a chain and computes the likelihood or posterior looping over all entries. It's possible to specify the columns, in case the input chain has different ordering, or larger number of parameters.

Parameters

input_dir	input directory
input_file	the input file
seed	the seed
column	the columns of the input file to be read
header_lines_to_skip	the lines to be skipped in the chain file
is_FITS_format	true \(\rightarrow\) the format of the input file is FITS; false \(\rightarrow\) the format of the input file is ASCII
apply_to_likelihood	true \(\rightarrow\) the likelihood ratio is used as weight; false \(\rightarrow\) the posterior ratio is used as weight

Warning: column is used only for ASCII chain files

Definition at line 240 of file Modelling.cpp.

◆ likelihood()

shared_ptr< statistics::Likelihood > cbl::modelling::Modelling::likelihood ( )

return the likelihood parameters

Returns: pointer to the likelihood parameters

Definition at line 72 of file Modelling.cpp.

◆ likelihood_parameters()

shared_ptr< cbl::statistics::ModelParameters > cbl::modelling::Modelling::likelihood_parameters ( )

return the likelihood parameters

Returns: pointer to the likelihood parameters

Definition at line 98 of file Modelling.cpp.

◆ m_set_posterior()

void cbl::modelling::Modelling::m_set_posterior ( const int seed )

set the interal variable m_posterior

Parameters

seed the seed

Definition at line 58 of file Modelling.cpp.

◆ m_set_prior()

void cbl::modelling::Modelling::m_set_prior ( std::vector< statistics::PriorDistribution > prior_distribution )

protected

set the internal variable m_parameter_priors

Parameters

prior_distribution vector containing the prior distributions

Definition at line 46 of file Modelling.cpp.

◆ maximize_likelihood()

void cbl::modelling::Modelling::maximize_likelihood	(	const std::vector< double >	start,
		const std::vector< std::vector< double >>	parameter_limits,
		const unsigned int	max_iter = `10000`,
		const double	tol = `1.e-6`,
		const double	epsilon = `1.e-3`
	)

function that maximizes the posterior, finds the best-fit parameters and stores them in the model

this function exploits the Nelder-Mead method https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method

the algorithm defines a simplex (i.e a k-dimensional polytope which is the convex hull of its k+1 vertices) in the parameter space. At each step, it identifies the simplex vertex at which the function to be minimised (i.e. the negative likelihood in this case) has the greatest value, and moves it, via reflections and scaling, to a new position in which the function has a lower value. This iteration stops when the simplex area becomes lower than the tolerance. For instance, in 2D, the starting vertices of the simplex (a triangle in 2D) are the following: (start[0], start[1]) ; (start[0]+epsilon, start[1]) ; (start[0], start[1]+epsilon)

Parameters

start	std::vector containing the initial values for the likelihood maximization
parameter_limits	limits of the parameter space in where the maximum of likelihood will be searched
max_iter	the maximum number of iterations
tol	the tolerance in finding convergence
epsilon	the simplex side

Definition at line 168 of file Modelling.cpp.

◆ maximize_posterior()

void cbl::modelling::Modelling::maximize_posterior	(	const std::vector< double >	start,
		const unsigned int	max_iter = `10000`,
		const double	tol = `1.e-6`,
		const double	epsilon = `1.e-3`,
		const int	seed = `666`
	)

function that maximizes the posterior, finds the best-fit parameters and stores them in the model

this function exploits the Nelder-Mead method https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method

the algorithm defines a simplex (i.e a k-dimensional polytope which is the convex hull of its k+1 vertices) in the parameter space. At each step, it identifies the simplex vertex at which the function to be minimised (i.e. the negative posterior in this case) has the greatest value, and moves it, via reflections and scaling, to a new position in which the function has a lower value. This iteration stops when the simplex area becomes lower than the tolerance. For instance, in 2D, the starting vertices of the simplex (a triangle in 2D) are the following: (start[0], start[1]) ; (start[0]+epsilon, start[1]) ; (start[0], start[1]+epsilon)

Parameters

start	vector containing initial values for the posterior maximization
max_iter	the maximum number of iterations
tol	the tolerance to find convergence
epsilon	the relative fraction of the initial simplex size
seed	the seed

Examples: model_2pt_monopole_RSD.cpp, model_2pt_multipoles.cpp, model_power_spectrum_angular.cpp, and modelling_VoidAbundances.cpp.

Definition at line 177 of file Modelling.cpp.

◆ posterior()

shared_ptr< cbl::statistics::Posterior > cbl::modelling::Modelling::posterior ( )

return the posterior parameters

Returns: pointer to the posterior parameters

Examples: model_2pt_multipoles.cpp.

Definition at line 85 of file Modelling.cpp.

◆ posterior_parameters()

shared_ptr< cbl::statistics::ModelParameters > cbl::modelling::Modelling::posterior_parameters ( )

return the posterior parameters

Returns: pointer to the posterior parameters

Definition at line 111 of file Modelling.cpp.

◆ read_chain()

void cbl::modelling::Modelling::read_chain	(	const std::string	input_dir,
		const std::string	input_file,
		const int	nwalkers,
		const std::vector< size_t >	columns = `{}`,
		const int	skip_header = `1`,
		const bool	fits = `false`
	)

read the chains

Parameters

input_dir	the input directory
input_file	the input file
nwalkers	the number of parallel chains
columns	the columns of the input file to be read.
skip_header	the lines to be skipped in the chain file
fits	false \(\rightarrow\) ascii file; true \(\rightarrow\) fits file

Definition at line 259 of file Modelling.cpp.

◆ reduced_chi2()

double cbl::modelling::Modelling::reduced_chi2 ( const std::vector< double > parameter = {} )

the reduced \(\chi^2\)

this function computes the reduced \(\chi^2\), i.e. \(\chi^2/(N_{\rm bins}-N_{\rm parameters})\)

Parameters

parameter vector containing the model parameters; if not provided in input, the chi2 is evaluated at best-fit parameter values

Returns: the reduced \(\chi^2\)

Definition at line 293 of file Modelling.cpp.

◆ reset_fit_range()

void cbl::modelling::Modelling::reset_fit_range ( )

inline

reset the fit range

set m_fit_range = false, that means that the fit range is unset

Definition at line 230 of file Modelling.h.

◆ sample_posterior() [1/5]

void cbl::modelling::Modelling::sample_posterior	(	const int	chain_size,
		const int	nwalkers,
		const double	radius,
		const std::vector< double >	start,
		const unsigned int	max_iter = `10000`,
		const double	tol = `1.e-6`,
		const double	epsilon = `1.e-3`,
		const int	seed = `666`,
		const double	aa = `2`,
		const bool	parallel = `true`
	)

sample the posterior, initializing the chains in a ball around the posterior best-fit parameters values

the starting values of the chain are extracted from uniform distributions in the range [parameter-radius, parameter+radius] (for each likelihood parameter)

this function first maximizes the posterior, starting the computation at the values of the input vector 'start', then it inizializes the chain

Parameters

chain_size	the chain lenght
nwalkers	the number of parallel chains
radius	radius of the ball in parameter space
start	std::vector containing initial values for the posterior maximization
max_iter	the maximum number of iterations
tol	the tolerance in finding convergence
epsilon	the simplex side
seed	the seed
aa	the parameter of the \(g(z)\) distribution
parallel	false \(\rightarrow\) non-parallel sampler; true \(\rightarrow\) parallel sampler

Definition at line 197 of file Modelling.cpp.

◆ sample_posterior() [2/5]

void cbl::modelling::Modelling::sample_posterior	(	const int	chain_size,
		const int	nwalkers,
		const int	seed = `666`,
		const double	aa = `2`,
		const bool	parallel = `true`
	)

sample the posterior, initializing the chains by drawing from the prior distributions

the starting values of the chain are extracted from the (possibly different) distributions of the priors

Parameters

chain_size	the chain lenght
nwalkers	the number of parallel chains
seed	the seed
aa	the parameter of the \(g(z)\) distribution
parallel	false \(\rightarrow\) non-parallel sampler; true \(\rightarrow\) parallel sampler

Examples: model_2pt_2D.cpp, model_2pt_monopole_BAO.cpp, model_2pt_monopole_RSD.cpp, model_2pt_projected.cpp, model_3pt.cpp, and model_cosmology.cpp.

Definition at line 187 of file Modelling.cpp.

◆ sample_posterior() [3/5]

void cbl::modelling::Modelling::sample_posterior	(	const int	chain_size,
		const int	nwalkers,
		const std::string	input_dir,
		const std::string	input_file,
		const int	seed = `666`,
		const double	aa = `2`,
		const bool	parallel = `true`
	)

sample the posterior, initializing the chains reading the input values from an input file

the starting values of the chain are get from the last lines of an input chain file; it can be used to continue an MCMC sampling computation

Parameters

chain_size	the chain lenght
nwalkers	the number of parallel chains
input_dir	input directory
input_file	the input file
seed	the seed
aa	the parameter of the \(g(z)\) distribution
parallel	false \(\rightarrow\) non-parallel sampler; true \(\rightarrow\) parallel sampler

Definition at line 229 of file Modelling.cpp.

◆ sample_posterior() [4/5]

void cbl::modelling::Modelling::sample_posterior	(	const int	chain_size,
		const int	nwalkers,
		std::vector< double > &	value,
		const double	radius,
		const int	seed = `666`,
		const double	aa = `2`,
		const bool	parallel = `true`
	)

sample the posterior, initializing the chains by drawing from the prior distributions

the starting values of the chain are extracted from the (possibly different) distributions of the priors

Parameters

chain_size	the chain lenght
nwalkers	the number of parallel chains
value	input values, center of the ball in parameter space
radius	radius of the ball in parameter space
seed	the seed
aa	the parameter of the \(g(z)\) distribution
parallel	false \(\rightarrow\) non-parallel sampler; true \(\rightarrow\) parallel sampler

Definition at line 207 of file Modelling.cpp.

◆ sample_posterior() [5/5]

void cbl::modelling::Modelling::sample_posterior	(	const int	chain_size,
		const std::vector< std::vector< double >>	chain_value,
		const int	seed = `666`,
		const double	aa = `2`,
		const bool	parallel = `true`
	)

sample the posterior, initializing the chains with input values

the starting values of the chain are the elements of the input matrix 'chain_values'

Parameters

chain_size	the chain lenght
chain_value	std::vector of size (nwalkers, nparameters) starting values of the chain
seed	the seed
aa	the parameter of the \(g(z)\) distribution
parallel	false \(\rightarrow\) non-parallel sampler; true \(\rightarrow\) parallel sampler

Definition at line 218 of file Modelling.cpp.

◆ set_data()

void cbl::modelling::Modelling::set_data ( const std::shared_ptr< data::Data > dataset )

inline

set the dataset

Parameters

dataset the dataset

Definition at line 259 of file Modelling.h.

◆ set_fit_range() [1/2]

void cbl::modelling::Modelling::set_fit_range	(	const double	xmin,
		const double	xmax
	)

set the fit range

Parameters

xmin	minimum x value used for the fit
xmax	maximum x value used for the fit

Examples: model_2pt_2D.cpp, model_2pt_monopole_BAO.cpp, model_2pt_monopole_RSD.cpp, model_2pt_projected.cpp, model_3pt.cpp, model_cosmology.cpp, and model_power_spectrum_angular.cpp.

Definition at line 46 of file Modelling1D.cpp.

◆ set_fit_range() [2/2]

void cbl::modelling::Modelling::set_fit_range	(	const double	xmin,
		const double	xmax,
		const double	ymin,
		const double	ymax
	)

set the fit range

Parameters

xmin	minimum x value used for the fit
xmax	maximum x value used for the fit
ymin	minimum y value used for the fit
ymax	maximum y value used for the fit

Definition at line 45 of file Modelling2D.cpp.

◆ set_likelihood() [1/2]

void cbl::modelling::Modelling::set_likelihood ( const cbl::statistics::Likelihood_function log_likelihood_function )

set the likelihood function, given a user-defined log-likelihood function

if the input parameter Nres is larger than 0, the inverted covariance matrix is corrected as follows (Hartlap, Simon and Schneider 2006):

\[ \hat{C}^{-1} = \left(1-\frac{n_b+1}{N_{res}-1}\right)C^{-1} \]

where \(n_b\) is the number of bins and \(N_{res}\) is the number of resamplings

Parameters

log_likelihood_function the user-defined loglikelihood function (natural logarithm)

Definition at line 146 of file Modelling.cpp.

◆ set_likelihood() [2/2]

void cbl::modelling::Modelling::set_likelihood	(	const statistics::LikelihoodType	likelihood_type,
		const std::vector< size_t >	x_index = `{0, 2}`,
		const int	w_index = `-1`,
		const double	prec = `1.e-10`,
		const int	Nres = `-1`
	)

set the likelihood function

if the input parameter Nres is larger than 0, the inverted covariance matrix is corrected as follows (Hartlap, Simon and Schneider 2006):

\[ \hat{C}^{-1} = \left(1-\frac{n_b+1}{N_{res}-1}\right)C^{-1} \]

where \(n_b\) is the number of bins and \(N_{res}\) is the number of resamplings

Parameters

likelihood_type	the likelihood type, specified with the LikelihoodType object
x_index	index(s) of the extra info std::vector containing the point(s) where to evaluate the model
w_index	index of the extra info std::vector containing the data point weight
prec	the precision required in the inversion of the covariance matrix
Nres	\(N_{res}\), the number of catalogue resamplings used to estimate the covariance matrix; \(N_{res}=-1\) if the covariance matrix has not been estimated with resampling methods

Examples: model_2pt_2D.cpp, model_2pt_monopole_BAO.cpp, model_2pt_monopole_RSD.cpp, model_2pt_multipoles.cpp, model_2pt_projected.cpp, model_3pt.cpp, model_cosmology.cpp, model_power_spectrum_angular.cpp, and modelling_VoidAbundances.cpp.

Definition at line 124 of file Modelling.cpp.

◆ set_parameter_from_string()

virtual void cbl::modelling::Modelling::set_parameter_from_string	(	const std::string	parameter,
		const double	value
	)

inlinevirtual

set the value of a parameter providing its name string

Parameters

parameter	parameter name to set
value	the new value for the parameter

Definition at line 186 of file Modelling.h.

◆ show_results()

void cbl::modelling::Modelling::show_results	(	const int	start = `0`,
		const int	thin = `1`,
		const int	nbins = `50`,
		const bool	show_mode = `false`,
		const int	ns = `-1`
	)

show the results of the MCMC sampling on screen

if the covariance matrix has been estimated from a set of mock catalogues, and the input parameters ns ( \(n_s\), the number of samples used to estimate the covariance matrix) is provided (>0), then the parameter errors ( \(\sigma_p\)) will be corrected to take into account the uncertainities in the covariance estimate (Percival et al. 2014):

\[ \sigma_p = \sqrt{\frac{1+B(n_b-n_p)}{1+A+B(n_p+1)}} \]

where

\[ A = \frac{2}{(n_s-n_b-1)(n_s-n_b-4)} \,, \]

\[ B = \frac{(n_s-n_b-2)}{(n_s-n_b-1)(n_s-n_b-4)} \,, \]

where \(n_b\) is number of data measurements (e.g. the bins of the dataset).

This correction can be applied only if the likelihood is Gaussian. Morever, the inverce covariance matrix estimator has to be corrected to take into account the inverse Wishart distribution (Hartlap, Simon and Schneider 2006).

Parameters

start	the minimum chain position to be written
thin	the step used for dilution on screen
nbins	the number of bins
show_mode	true \(\rightarrow\) show the posterior mode; false \(\rightarrow\) do not show the posterior mode
ns	number of samples used to estimate the covariance matrix

Examples: model_2pt_2D.cpp, model_2pt_monopole_BAO.cpp, model_2pt_monopole_RSD.cpp, model_2pt_projected.cpp, model_3pt.cpp, and model_cosmology.cpp.

Definition at line 269 of file Modelling.cpp.

◆ write_chain()

void cbl::modelling::Modelling::write_chain	(	const std::string	output_dir,
		const std::string	output_file,
		const int	start = `0`,
		const int	thin = `1`,
		const bool	is_FITS_format = `false`,
		const int	prec = `5`,
		const int	ww = `14`
	)

write the chains obtained after the MCMC sampling

Parameters

output_dir	the output directory
output_file	the output file
start	the minimum chain position to be written
thin	the step used for dilution
is_FITS_format	true \(\rightarrow\) the format of the input file is FITS; false \(\rightarrow\) the format of the input file is ASCII
prec	decimal precision
ww	number of characters to be used as field width

Examples: model_2pt_2D.cpp.

Definition at line 250 of file Modelling.cpp.

◆ write_model() [1/2]

void cbl::modelling::Modelling::write_model	(	const std::string	output_dir,
		const std::string	output_file,
		const std::vector< double >	xx,
		const std::vector< double >	parameters
	)

virtual

write the model at xx for given parameters

Parameters

output_dir	the output directory
output_file	the output file
xx	vector of points at which the model is computed,
parameters	vector containing the input parameters used to compute the model; if this vector is not provided, the model will be computed using the best-fit parameters

Reimplemented in cbl::modelling::twopt::Modelling_TwoPointCorrelation_wedges.

Definition at line 56 of file Modelling1D.cpp.

◆ write_model() [2/2]

void cbl::modelling::Modelling::write_model	(	const std::string	output_dir,
		const std::string	output_file,
		const std::vector< double >	xx,
		const std::vector< double >	yy,
		const std::vector< double >	parameters
	)

virtual

write the model at xx, yy for given parameters

Parameters

output_dir	the output directory
output_file	the output file
xx	vector of points at which the model is computed, first axis
yy	vector of points at which the model is computed, second axis
parameters	vector containing the input parameters used to compute the model; if this vector is not provided, the model will be computed using the best-fit parameters

Definition at line 54 of file Modelling2D.cpp.

◆ write_model_at_bestfit() [1/2]

void cbl::modelling::Modelling::write_model_at_bestfit	(	const std::string	output_dir,
		const std::string	output_file,
		const std::vector< double >	xx
	)

virtual

write the model at xx with best-fit parameters obtained from posterior maximization

Parameters

output_dir	the output directory
output_file	the output file
xx	vector of points at which the model is computed

Reimplemented in cbl::modelling::twopt::Modelling_TwoPointCorrelation_wedges.

Examples: model_power_spectrum_angular.cpp.

Definition at line 68 of file Modelling1D.cpp.

◆ write_model_at_bestfit() [2/2]

void cbl::modelling::Modelling::write_model_at_bestfit	(	const std::string	output_dir,
		const std::string	output_file,
		const std::vector< double >	xx,
		const std::vector< double >	yy
	)

virtual

write the model at xx, yy with best-fit parameters obtained from likelihood maximization

Parameters

output_dir	the output directory
output_file	the output file
xx	vector of points at which the model is computed, first axis
yy	vector of points at which the model is computed, second axis

Definition at line 66 of file Modelling2D.cpp.

◆ write_model_from_chains() [1/2]

void cbl::modelling::Modelling::write_model_from_chains	(	const std::string	output_dir,
		const std::string	output_file,
		const std::vector< double >	xx,
		const int	start = `0`,
		const int	thin = `1`
	)

virtual

write the model at xx computing 16th, 50th and 84th percentiles from the chains

Parameters

output_dir	the output directory
output_file	the output file
xx	vector of points at which the model is computed
start	the starting position for each chain
thin	the position step

Reimplemented in cbl::modelling::twopt::Modelling_TwoPointCorrelation_wedges.

Examples: model_2pt_2D.cpp, and model_2pt_monopole_RSD.cpp.

Definition at line 80 of file Modelling1D.cpp.

◆ write_model_from_chains() [2/2]

void cbl::modelling::Modelling::write_model_from_chains	(	const std::string	output_dir,
		const std::string	output_file,
		const std::vector< double >	xx,
		const std::vector< double >	yy,
		const int	start = `0`,
		const int	thin = `1`
	)

virtual

write the model at xx, yy computing 16th, 50th and 84th percentiles from the chains

Parameters

output_dir	the output directory
output_file	the output file
xx	vector of points at which the model is computed, first axis
yy	vector of points at which the model is computed, second axis
start	the starting position for each chain
thin	the position step

Definition at line 78 of file Modelling2D.cpp.

◆ write_results()

void cbl::modelling::Modelling::write_results	(	const std::string	output_dir,
		const std::string	root_file,
		const int	start = `0`,
		const int	thin = `1`,
		const int	nbins = `50`,
		const bool	fits = `false`,
		const bool	compute_mode = `false`,
		const int	ns = `-1`
	)

write the results of the MCMC sampling to file

this function stores to file the posterior mean, the posterior standard deviation, the posterior median, 18th and 82th posterior percentiles, and, optionally, the posterior mode.

If the covariance matrix has been estimated from a set of mock catalogues, and the input parameters ns ( \(n_s\), the number of samples used to estimate the covariance matrix) is provided (>0), then the parameter errors ( \(\sigma_p\)) will be corrected to take into account the uncertainities in the covariance estimate (Percival et al. 2014):

\[ \sigma_p = \sqrt{\frac{1+B(n_b-n_p)}{1+A+B(n_p+1)}} \]

where

\[ A = \frac{2}{(n_s-n_b-1)(n_s-n_b-4)} \,, \]

\[ B = \frac{(n_s-n_b-2)}{(n_s-n_b-1)(n_s-n_b-4)} \,, \]

where \(n_b\) is number of data measurements (e.g. the bins of the dataset).

This correction can be applied only if the likelihood is Gaussian. Morever, the inverce covariance matrix estimator has to be corrected to take into account the inverse Wishart distribution (Hartlap, Simon and Schneider 2006).

Parameters

output_dir	the output director
root_file	the root of the output files: - file_root_parameters.dat file containing the output of the MCMC sampling for each parameter - file_root_covariance.dat file containing the covariance of the parameters - file_root_chain file containing the chains: the extention can be .dat or .fits
start	the minimum chain position to be written
thin	the step used for dilution on screen
nbins	the number of bins
fits	false \(\rightarrow\) ascii file; true \(\rightarrow\) fits file
compute_mode	true \(\rightarrow\) compute the posterior mode; false \(\rightarrow\) do not compute the posterior mode
ns	number of samples used to estimate the covariance matrix

Examples: model_2pt_monopole_RSD.cpp, model_2pt_projected.cpp, and model_3pt.cpp.

Definition at line 281 of file Modelling.cpp.

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

Headers/Modelling.h
Modelling/Global/Modelling.cpp
Modelling/Global/Modelling1D.cpp
Modelling/Global/Modelling2D.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Function Documentation

◆ data()

◆ data_fit()

◆ get_parameter_from_string()

◆ get_prior()

◆ get_response_function()

◆ importance_sampling()

◆ likelihood()

◆ likelihood_parameters()

◆ m_set_posterior()

◆ m_set_prior()

◆ maximize_likelihood()

◆ maximize_posterior()

◆ posterior()

◆ posterior_parameters()

◆ read_chain()

◆ reduced_chi2()

◆ reset_fit_range()

◆ sample_posterior() [1/5]

◆ sample_posterior() [2/5]

◆ sample_posterior() [3/5]

◆ sample_posterior() [4/5]

◆ sample_posterior() [5/5]

◆ set_data()

◆ set_fit_range() [1/2]

◆ set_fit_range() [2/2]

◆ set_likelihood() [1/2]

◆ set_likelihood() [2/2]

◆ set_parameter_from_string()

◆ show_results()

◆ write_chain()

◆ write_model() [1/2]

◆ write_model() [2/2]

◆ write_model_at_bestfit() [1/2]

◆ write_model_at_bestfit() [2/2]

◆ write_model_from_chains() [1/2]

◆ write_model_from_chains() [2/2]

◆ write_results()