#include "Headers/CombinedPosterior.h"

Inheritance diagram for cbl::statistics::CombinedPosterior:

Collaboration diagram for cbl::statistics::CombinedPosterior:

[legend]

Public Member Functions
void	set_log_posterior (const std::vector< double > logpostA, const std::vector< double > logpostB)
	set the internal values of m_log_posterior as the concatenation of the logposterior vectors of two cosmological chains More...

void	set_parameters (const std::vector< std::vector< double >> parametersA, const std::vector< std::vector< double >> parametersB)
	set the internal values of m_parameters as the concatenation of the parameters vectors of two cosmological chains More...

void	set_weight (const std::vector< double > weightsA, const std::vector< double > weightsB)
	set the internal values of m_weight as the concatenation of the weights vectors of two MCMC chains More...

void	m_check_repeated_par (int dummy_Nposteriors, std::vector< std::shared_ptr< Posterior >> posteriors, const std::vector< std::string > repeated_par)
	check the repeated parameters More...

void	m_check_common_repeated_par (int dummy_Nposteriors, std::vector< std::shared_ptr< Posterior >> posteriors, std::vector< std::string > repeated_par, std::vector< std::vector< std::vector< int >>> common_repeated_par)
	check the common repeated parameters More...

void	m_add_prior (bool par_is_repeated, std::vector< std::shared_ptr< Posterior >> posteriors, const int N, const int k, std::vector< std::shared_ptr< cbl::statistics::PriorDistribution >> &prior_distributions)
	add a prior More...

void	m_set_common_repeated_par (std::vector< std::shared_ptr< Posterior >> posteriors, const bool is_in_parnames, const int N, const int k, const std::vector< std::string > repeated_par, const std::vector< std::vector< std::vector< int >>> common_repeated_par, std::vector< std::shared_ptr< cbl::statistics::PriorDistribution >> &prior_distributions, std::vector< std::string > &parameter_names, std::vector< std::string > &original_names, std::vector< ParameterType > &parameter_types)
	set a common repeated parameter More...

void	m_set_repeated_par (std::vector< std::shared_ptr< Posterior >> posteriors, const bool is_in_parnames, const int N, const int k, const std::vector< std::string > repeated_par, const std::vector< std::vector< std::vector< int >>> common_repeated_par, std::vector< std::shared_ptr< cbl::statistics::PriorDistribution >> &prior_distributions, std::vector< std::string > &parameter_names, std::vector< std::string > &original_names, std::vector< ParameterType > &parameter_types)
	set a repeated parameter More...

void	m_set_parameters_priors (std::vector< std::shared_ptr< Posterior >> posteriors, std::vector< std::string > repeated_par={}, const std::vector< std::vector< std::vector< int >>> common_repeated_par={})
	set the parameters and the priors More...

void	m_set_independent_probes ()
	set all the internal variables needed for modelling independent probes

void	importance_sampling (const int distNum, const double cell_size, const double rMAX, const double cut_sigma=-1)
	do the importance sampling for two Posterior objects, which has been read externally More...

void	importance_sampling (const std::string output_path, const std::string model_nameA, const std::string model_nameB, const std::vector< double > start, const int chain_size, const int nwalkers, const int burn_in, const int thin)
	do the importance sampling for two Posterior objects, that are constructed from dataset and models More...

void	initialize_chains (const int chain_size, const int n_walkers, 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)
	initialize the chains in a ball around the posterior best-fit parameter values More...

void	initialize_chains (const int chain_size, const int n_walkers)
	initialize the chains in a ball around the posterior best-fit parameter values More...

void	initialize_chains (const int chain_size, const int n_walkers, const std::string input_dir, const std::string input_file, const int seed)
	initialize the chains reading the input values from an input file More...

void	sample_stretch_move (const double aa=2, const bool parallel=true, const std::string outputFile=par::defaultString, const int start=0, const int thin=1, const int nbins=50)
	sample the posterior using the stretch-move sampler (Foreman-Mackey et al. 2012) More...

double	operator() (std::vector< double > &pp) const
	evaluate the un-normalized posterior as the product of the un-normalized entry posteriors. For N Posterior objects, at a given point \( \vec{\theta_i} \) in the parameter space: More...

double	log (std::vector< double > &pp) const
	evaluate the logarithm of the un-normalized posterior as the sum of all the logarithm of the un-normalized posteriors of the N entry objects. Considering a given point \( \vec{\theta_i} \) in the parameter space: More...

void	maximize (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 store them in the model More...

void	maximize (const std::vector< double > start, const unsigned int max_iter=10000, const double tol=1.e-6, const double epsilon=1.e-4)
	function that maximize the posterior, find the best-fit parameters and store them in model 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, const int nb=-1)
	store the results of the MCMC sampling to file More...

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

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	write_chain_ascii (const std::string output_dir, const std::string output_file, const int start=0, const int thin=1, const int prec=5, const int ww=14)
	write the chains obtained after the MCMC sampling on an ascii file More...

void	write_chain_fits (const std::string output_dir, const std::string output_file, const int start=0, const int thin=1)
	write the chains obtained after the MCMC sampling on a FITS file More...

void	write_model_from_chain (const std::string output_dir, const std::string output_file, const int start, const int thin, const std::vector< double > xx={}, const std::vector< double > yy={})
	write the model computing 16th, 50th and 84th percentiles from the MCMC More...

void	write_maximization_results (const std::string dir_output, const std::string file)
	write maximization results on a file More...

std::vector< std::vector< double > >	read (const std::string path, const std::string filename)
	read an entire 2d table data (MCMC chain) of unknown dimension More...

Constructors/destructors
	CombinedPosterior ()=default
	default constructor

	CombinedPosterior (const std::vector< std::shared_ptr< Posterior >> posteriors, std::vector< std::string > repeated_par={}, const std::vector< std::vector< std::vector< int >>> common_repeated_par={})
	Constructor used to set the modelling of statistically independent probes, or used to perform importance sampling. More...

	CombinedPosterior (const std::vector< std::vector< std::shared_ptr< Posterior >>> posteriors, const std::vector< std::shared_ptr< data::CovarianceMatrix >> covariance, const std::vector< cbl::statistics::LikelihoodType > likelihood_types, const std::vector< std::string > repeated_par={}, const std::vector< std::vector< std::vector< int >>> common_repeated_par={}, const std::vector< std::shared_ptr< cbl::cosmology::SuperSampleCovariance >> SSC={})
	Constructor used to set the modelling of statistically dependent probes. For each vector of cbl::statistics::Posterior objects in the posteriors argument, a cbl::data::CovarianceMatrix object must be defined. The probes in each vector within posteriors are described by the same likelihood function. The final log-likelihood is given by the sum of the logarithms of each likelihood describing a set of dependent probes. More...

	~CombinedPosterior ()=default
	default destructor

Public Member Functions inherited from cbl::statistics::Posterior
std::shared_ptr< ModelParameters >	parameters () const
	return the posterior parameters More...

double	operator() (std::vector< double > &pp) const
	the un-normalized posterior More...

std::vector< double >	weight (const int start=0, const int thin=1) const
	return the internal member m_weights More...

double	log (std::vector< double > &pp) const
	the logarithm of the un-normalized posterior More...

double	chi2 (const std::vector< double > parameter={}) const
	the \(\chi^2\) More...

void	set_model (std::shared_ptr< Model > model=NULL, const std::shared_ptr< ModelParameters > model_parameters=NULL)
	set the model for the posterior analysis More...

void	set (const std::vector< std::shared_ptr< PriorDistribution >> prior_distributions, const std::shared_ptr< data::Data > data, const std::shared_ptr< Model > model, const LikelihoodType likelihood_type, const std::vector< size_t > x_index, const int w_index, const int seed)
	set the posterior type using the LikelihoodType object More...

int	get_Nparameters ()
	get the number of parameters used More...

int	m_get_seed ()
	get the value of the internal variable m_seed More...

bool	get_m_use_grid ()
	get the value of the internal variable m_use_grid More...

std::vector< std::vector< double > >	get_parameters ()
	get the values of the internal variable m_parameters More...

std::vector< double >	get_log_posterior ()
	get the values of the internal variable m_log_posterior More...

std::shared_ptr< void >	get_m_likelihood_inputs ()
	get the values of the internal variable m_likelihood_inputs More...

std::shared_ptr< cbl::statistics::Prior >	get_m_prior ()
	get the values of the internal variable m_prior More...

LogLikelihood_function	get_m_log_likelihood_function ()
	get the values of the internal variable m_log_likelihood_function More...

Likelihood_function	get_m_likelihood_function ()
	get the values of the internal variable m_likelihood_function More...

Likelihood_function	get_m_likelihood_function_grid ()
	get the values of the internal variable m_likelihood_function_grid More...

LogLikelihood_function	get_m_log_likelihood_function_grid ()
	get the values of the internal variable m_log_likelihood_function_grid More...

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

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

void	maximize (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 store them in the model More...

void	maximize (const std::vector< double > start, const unsigned int max_iter=10000, const double tol=1.e-6, const double epsilon=1.e-4)
	function that maximize the posterior, find the best-fit parameters and store them in model More...

void	initialize_chains (const int chain_size, const int n_walkers)
	initialize the chains by drawing from the prior distributions More...

void	initialize_chains (const int chain_size, const int n_walkers, 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)
	initialize the chains in a ball around the posterior best-fit parameter values More...

void	initialize_chains (const int chain_size, const int n_walkers, std::vector< double > &value, const double radius)
	initialize the chains in a ball around the input parameter values More...

void	initialize_chains (const int chain_size, const std::vector< std::vector< double >> chain_value)
	initialize the chains with input values More...

void	initialize_chains (const int chain_size, const int n_walkers, const std::string input_dir, const std::string input_file)
	initialize the chains reading from an input file More...

void	sample_stretch_move (const double aa=2, const bool parallel=true, const std::string outputFile=par::defaultString, const int start=0, const int thin=1, const int nbins=50)
	sample the posterior using the stretch-move sampler (Foreman-Mackey et al. 2012) More...

void	importance_sampling (const std::string input_dir, const std::string input_file, 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, const int n_walkers=100)
	perform importance sampling More...

void	read_chain (const std::string input_dir, const std::string input_file, const int n_walkers, const std::vector< size_t > column={}, const int header_lines_to_skip=1, const bool is_FITS_format=false)
	read the chains More...

void	read_chain_ascii (const std::string input_dir, const std::string input_file, const int n_walkers, const std::vector< size_t > column={}, const int header_lines_to_skip=1)
	read the chains from an ascii file More...

void	read_chain_fits (const std::string input_dir, const std::string input_file, const int n_walkers, const std::vector< size_t > column)
	read the chains from an ascii file More...

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	write_chain_ascii (const std::string output_dir, const std::string output_file, const int start=0, const int thin=1, const int prec=5, const int ww=14)
	write the chains obtained after the MCMC sampling on an ascii file More...

void	write_chain_fits (const std::string output_dir, const std::string output_file, const int start=0, const int thin=1)
	write the chains obtained after the MCMC sampling on a FITS file More...

void	write_maximization_results (const std::string output_dir, const std::string root_file)
	write maximization results on a file More...

void	show_results (const int start, const int thin, const int nbins=50, const bool show_mode=false, const int ns=-1, const int nb=-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, const int nb=-1)
	store the results of the MCMC sampling to file More...

void	write_model_from_chain (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 MCMC chains More...

	Posterior ()=default
	default constructor

	Posterior (const std::vector< std::shared_ptr< PriorDistribution >> prior_distributions, const Likelihood &likelihood, const int seed=5341)
	constructor More...

	Posterior (const std::vector< std::shared_ptr< PriorDistribution >> prior_distributions, const std::shared_ptr< data::Data > data, const std::shared_ptr< Model > model, const LikelihoodType likelihood_type, const std::vector< size_t > x_index, const int w_index, const int seed=5341)
	constructor More...

	Posterior (const std::string file_name, const std::string path_file, const std::vector< int > usecols, const std::vector< std::string > parameter_names, const int skip_header)
	constructor More...

	~Posterior ()=default
	default destructor

Public Member Functions inherited from cbl::statistics::Likelihood
std::shared_ptr< ModelParameters >	parameters () const
	return the likelihood parameters More...

double	operator() (std::vector< double > &pp) const
	evaluate the likelihood More...

double	log (std::vector< double > &parameter) const
	evaluate the logarithm of the likelihood for the input parameters More...

void	set_data (std::shared_ptr< data::Data > data)
	set the data for the likelihood analysis More...

void	set_model (std::shared_ptr< Model > model=NULL, const std::shared_ptr< ModelParameters > model_parameters=NULL)
	set the model for the likelihood analysis More...

void	unset_grid ()
	set the likelihood function with internal values of LikelihoodType

std::shared_ptr< Model >	get_m_model ()
	get the values of the internal variable m_model More...

std::shared_ptr< ModelParameters >	get_model_parameters ()
	get the values of the internal variable m_model More...

std::shared_ptr< data::Data >	get_m_data ()
	get the values of the internal variable m_data More...

void	set_grid (const int npoints, const std::vector< std::vector< double >> parameter_limits, const std::string file, const bool read=false)
	set the likelihood function as a grid, to speed up computation: this only works for one or two free parameters More...

void	set_function (const 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 type using the LikelihoodType object More...

void	set_function (const LogLikelihood_function likelihood_function)
	set the likelihood function More...

void	set_log_function (const LogLikelihood_function loglikelihood_function)
	set the natural logarithm of the likelihood function More...

void	write_results (const std::string dir_output, const std::string file)
	write best-fit results on a file More...

void	maximize (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 likelihood, finds the best-fit parameters and stores them in the model More...

void	write_model (const std::string output_dir, const std::string output_file, const std::vector< double > parameters, const std::vector< double > xx={}, const std::vector< double > yy={})
	write the model at xx at bestfit More...

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 at bestfit More...

	Likelihood ()
	default constructor

	Likelihood (const std::shared_ptr< data::Data > data, const std::shared_ptr< Model > model, const LikelihoodType likelihood_type, const std::vector< size_t > x_index={0, 2}, const int w_index=-1, const std::shared_ptr< ModelParameters > model_parameters=NULL, const double prec=1.e-10, const int Nres=-1)
	constructor More...

	Likelihood (const std::shared_ptr< data::Data > data, const std::shared_ptr< Model > model, const Likelihood_function log_likelihood_function, const std::shared_ptr< ModelParameters > model_parameters=NULL)
	constructor More...

virtual	~Likelihood ()=default
	default destructor

Private Attributes
STR_DependentProbes_data_model	m_data_model
	the container of parameters for statistically dependent probes

std::vector< std::shared_ptr< Posterior > >	m_posteriors
	shared pointers vector containing input Posterior objects

int	m_Nposteriors
	number of posteriors

std::vector< std::vector< int > >	m_parameter_indexes
	indexes of the parameters, for each posterior object, in the total parameter vector

std::vector< std::vector< int > >	m_parameter_indexes2
	indexes of the parameters, for each posterior object, in the total parameter vector

std::vector< int >	m_cosmoPar_indexes
	indexes of the cosmological parameters

std::vector< std::vector< std::string > >	m_parameter_names
	names of the parameters, for each posterior object

bool	impsampling = false
	importance sampling mode

std::vector< std::shared_ptr< void > >	m_likelihood_inputs
	likelihood inputs

std::vector< LogLikelihood_function >	m_log_likelihood_functions
	log-likelihood functions

std::vector< Likelihood_function >	m_likelihood_functions
	likelihood functions

std::vector< LogLikelihood_function >	m_likelihood_functions_grid
	likelihood functions on a grid

std::vector< LogLikelihood_function >	m_log_likelihood_functions_grid
	log-likelihood functions on a grid

std::vector< std::shared_ptr< data::Data > >	m_datasets
	data containers

std::vector< std::shared_ptr< Model > >	m_models
	models to test

std::vector< bool >	m_use_grid
	use_grid vector

Additional Inherited Members
Protected Member Functions inherited from cbl::statistics::Posterior
void	m_set_seed (const int seed)
	set the internal attribute m_seed and related quantities More...

int	m_generate_seed ()
	generate a seed More...

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

Protected Member Functions inherited from cbl::statistics::Likelihood
void	m_set_grid_likelihood_1D (const int npoints, const std::vector< std::vector< double >> parameter_limits, const std::string output_file)
	set the likelihood grid and write the grid on a file More...

void	m_set_grid_likelihood_1D (const std::string input_file)
	set the likelihood grid from file More...

void	m_set_grid_likelihood_2D (const int npoints, const std::vector< std::vector< double >> parameter_limits, const std::string output_file)
	set the likelihood grid and write the grid on a file More...

void	m_set_grid_likelihood_2D (const std::string input_file)
	set the likelihood grid from file More...

Protected Attributes inherited from cbl::statistics::Posterior
std::shared_ptr< cbl::statistics::Prior >	m_prior
	the prior distribution

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

std::vector< double >	m_log_likelihood
	the logarithm of the likelihood

std::vector< double >	m_acceptance
	the MCMC acceptance rate

int	m_seed
	general seed for prior/posterior distribution and sampler

std::shared_ptr< cbl::random::UniformRandomNumbers_Int >	m_seed_generator
	seed generator

std::vector< double >	m_log_posterior
	the logarithm of the posterior

int	m_Nparameters
	the number of parameters

std::vector< std::vector< double > >	m_parameters
	the parameters

std::vector< double >	m_weight
	the chain weight

Protected Attributes inherited from cbl::statistics::Likelihood
std::shared_ptr< data::Data >	m_data
	data containers

std::shared_ptr< Model >	m_model
	model to test

std::shared_ptr< void >	m_likelihood_inputs
	likelihood inputs

std::shared_ptr< ModelParameters >	m_model_parameters
	likelihood parameters

LikelihoodType	m_likelihood_type = LikelihoodType::_NotSet_
	type of the likelihood

LogLikelihood_function	m_log_likelihood_function
	log-likelihood function

Likelihood_function	m_likelihood_function
	likelihood function

LogLikelihood_function	m_likelihood_function_grid
	likelihood function on a grid

LogLikelihood_function	m_log_likelihood_function_grid
	log-likelihood function on a grid

std::vector< size_t >	m_x_index

int	m_w_index
	the index in extra info where the bin weight is stored

bool	m_use_grid = false
	use grid

Detailed Description

The class CombinedPosterior.

This class is used to define the distribution

Definition at line 105 of file CombinedPosterior.h.

Constructor & Destructor Documentation

◆ CombinedPosterior() [1/2]

cbl::statistics::CombinedPosterior::CombinedPosterior	(	const std::vector< std::shared_ptr< Posterior >>	posteriors,
		std::vector< std::string >	repeated_par = `{}`,
		const std::vector< std::vector< std::vector< int >>>	common_repeated_par = `{}`
	)

Constructor used to set the modelling of statistically independent probes, or used to perform importance sampling.

Parameters

posteriors	pointers to Posterior objects
repeated_par	parameters shared by different probes, for which the user wants different posteriors for each probe. For example, if the probes A and B depend on the same parameter \(p\), whose identification string is "par", then "par" must be given in input if the user desires to have different posteriors of \(p\) for the two probes A and B. Every probe depending on \(p\) will provide a different posterior on \(p\). This is useful in the case of astrophysical parameters, e.g. the parameters describing galaxy cluster profiles.
common_repeated_par	for each argument in repeated_par, a vector of vectors of integers can be defined here. Such vectors define the sets of probes for which the same priors and posteriors are provided for the same parameters. For example, let us consider the probes {A1, A2, A3, A4}, provided in the posteriors parameter. All the probes (A1, A2, A3, A4) depend on the parameter \(p\), whose identification string is "par", and we set repeated_par = {"par"}. If we want the pair of probes {A1, A2}, {A3, A4}, to provide a different posterior on \(p\), we must set common_repeated_par = { { {0,1}, {2,3} } }. This is useful when different probes in the same bin provide constraints on the same parameters. If common_repeated_par is not provided, every probe depending on \(p\) will provide a different posterior on \(p\). If two parameters are provided in repeated_par, e.g. repeated_par = {"par1", "par2"}, and only "par2" must be shared by more than one probe, then leave blank the vector of vectors corresponding to "par1" in common_repeated_par.

Definition at line 47 of file CombinedPosterior.cpp.

◆ CombinedPosterior() [2/2]

cbl::statistics::CombinedPosterior::CombinedPosterior	(	const std::vector< std::vector< std::shared_ptr< Posterior >>>	posteriors,
		const std::vector< std::shared_ptr< data::CovarianceMatrix >>	covariance,
		const std::vector< cbl::statistics::LikelihoodType >	likelihood_types,
		const std::vector< std::string >	repeated_par = `{}`,
		const std::vector< std::vector< std::vector< int >>>	common_repeated_par = `{}`,
		const std::vector< std::shared_ptr< cbl::cosmology::SuperSampleCovariance >>	SSC = `{}`
	)

Constructor used to set the modelling of statistically dependent probes. For each vector of cbl::statistics::Posterior objects in the posteriors argument, a cbl::data::CovarianceMatrix object must be defined. The probes in each vector within posteriors are described by the same likelihood function. The final log-likelihood is given by the sum of the logarithms of each likelihood describing a set of dependent probes.

If sets of probes are described by user-defined likelihoods, then the cbl::data::CovarianceMatrix objects must not be provided for such sets.

Parameters

posteriors	vector of vectors of pointers to Posterior objects. In each vector, a set of probes is contained, with a covariance matrix defined by the corresponding cbl::data::CovarianceMatrix object given as input in the second argument of this constructor
covariance	objects defining the covariance matrices for the Posterior objects given in input
likelihood_types	likelihood types describing each set of probes
repeated_par	parameters shared by different probes, for which the user wants different posteriors for each probe. For example, if the probes A and B depend on the same parameter \(p\), whose identification string is "par", then "par" must be given in input if the user desires to have different posteriors of \(p\) for the two probes A and B. This is useful in the case of astrophysical parameters, e.g. the parameters describing galaxy cluster profiles.
common_repeated_par	for each argument in repeated_par, a vector of vectors of integers can be defined here. Such vectors define the sets of probes for which the same priors and posteriors are provided for the same parameters. For example, let us consider the two sets of probes {A1, A2, A3} and {B1, B2, B3}, provided in the posteriors parameter. All the probes (A1, A2, A3, B1, B2, B3) depend on the parameter \(p\), whose identification string is "par", and we set repeated_par = {"par"}. If we want each pair of probes {A1, B1}, {A2, B2}, {A3, B3}, to provide a different posterior on \(p\), we must set common_repeated_par = { { {0,3}, {1,4}, {2,5} } }. This is useful when different probes in the same bin provide constraints on the same parameters. If common_repeated_par is not provided, every probe depending on \(p\) will provide a different posterior on \(p\). If two parameters are provided in repeated_par, e.g. repeated_par = {"par1", "par2"}, and only "par2" must be shared by more than one probe, then leave blank the vector of vectors corresponding to "par1" in common_repeated_par.
SSC	vector of pointers to cbl::cosmology::SuperSampleCovariance objects, for the computation of the \(S_{ij}\) matrices. If, for example, the sets of probes A, B, C, are considered, and only for A and C the super-sample covariance must be computed, then set the second element of SSC equal to NULL.

Definition at line 81 of file CombinedPosterior.cpp.

Member Function Documentation

◆ importance_sampling() [1/2]

void cbl::statistics::CombinedPosterior::importance_sampling	(	const int	distNum,
		const double	cell_size,
		const double	rMAX,
		const double	cut_sigma = `-1`
	)

do the importance sampling for two Posterior objects, which has been read externally

Parameters

distNum	number of points for the averaging
cell_size	cell dimension
rMAX	searching radius
cut_sigma	for the weight's distribution cut

Definition at line 662 of file CombinedPosterior.cpp.

◆ importance_sampling() [2/2]

void cbl::statistics::CombinedPosterior::importance_sampling	(	const std::string	output_path,
		const std::string	model_nameA,
		const std::string	model_nameB,
		const std::vector< double >	start,
		const int	chain_size,
		const int	nwalkers,
		const int	burn_in,
		const int	thin
	)

do the importance sampling for two Posterior objects, that are constructed from dataset and models

Parameters

output_path	the path where the chains will be stored
model_nameA	the name of the first model
model_nameB	the name of the second model
start	std::vector containing initial values for the posterior maximization
chain_size	the size of the chains that has to be ran
nwalkers	the number of parallal walkers for the chain
burn_in	the minimum chain position to be written
thin	the step used for dilution on screen

Definition at line 713 of file CombinedPosterior.cpp.

◆ initialize_chains() [1/3]

void cbl::statistics::CombinedPosterior::initialize_chains	(	const int	chain_size,
		const int	n_walkers
	)

initialize the chains in a ball around the posterior best-fit parameter 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
n_walkers	the number of parallel chains

Definition at line 779 of file CombinedPosterior.cpp.

◆ initialize_chains() [2/3]

void cbl::statistics::CombinedPosterior::initialize_chains	(	const int	chain_size,
		const int	n_walkers,
		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`
	)

initialize the chains in a ball around the posterior best-fit parameter 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
n_walkers	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

Definition at line 768 of file CombinedPosterior.cpp.

◆ initialize_chains() [3/3]

void cbl::statistics::CombinedPosterior::initialize_chains	(	const int	chain_size,
		const int	n_walkers,
		const std::string	input_dir,
		const std::string	input_file,
		const int	seed
	)

initialize the chains reading the input values from an input file

Parameters

chain_size	the chain lenght
n_walkers	the number of parallel chains
input_dir	input directory
input_file	input file
seed	the seed

Definition at line 789 of file CombinedPosterior.cpp.

◆ log()

double cbl::statistics::CombinedPosterior::log ( std::vector< double > & pp ) const

evaluate the logarithm of the un-normalized posterior as the sum of all the logarithm of the un-normalized posteriors of the N entry objects. Considering a given point \( \vec{\theta_i} \) in the parameter space:

\[ P(\vec{\theta_i} | \vec{d}) = \sum_{j=1}^{N} \log{\mathcal{L_j}(\vec{d}|\vec{\theta_i})} + \log{Pr(\vec{\theta_i})} \]

where \(P\) is the combined posterior, \(\mathcal{L_j}(\vec{d}|\vec{\theta})\) is the j-th likelihood function and \(Pr(\vec{\theta})\) is the prior distribution.

Parameters

pp	the parameters

Returns: the logarithm of the un-normalized posterior

Definition at line 914 of file CombinedPosterior.cpp.

◆ m_add_prior()

void cbl::statistics::CombinedPosterior::m_add_prior	(	bool	par_is_repeated,
		std::vector< std::shared_ptr< Posterior >>	posteriors,
		const int	N,
		const int	k,
		std::vector< std::shared_ptr< cbl::statistics::PriorDistribution >> &	prior_distributions
	)

add a prior

Parameters

par_is_repeated	if true, the considered parameter is repeated
posteriors	pointer to the Posterior objects
N	index of the Posterior object
k	index of the parameter of the N-th Posterior
prior_distributions	vector containing all the Posterior objects

Definition at line 337 of file CombinedPosterior.cpp.

◆ m_check_common_repeated_par()

void cbl::statistics::CombinedPosterior::m_check_common_repeated_par	(	int	dummy_Nposteriors,
		std::vector< std::shared_ptr< Posterior >>	posteriors,
		std::vector< std::string >	repeated_par,
		std::vector< std::vector< std::vector< int >>>	common_repeated_par
	)

check the common repeated parameters

Parameters

dummy_Nposteriors	number of posterior objects
posteriors	vector of input Posterior objects
repeated_par	repeated parameters
common_repeated_par	indices of the common repeated parameters

Definition at line 309 of file CombinedPosterior.cpp.

◆ m_check_repeated_par()

void cbl::statistics::CombinedPosterior::m_check_repeated_par	(	int	dummy_Nposteriors,
		std::vector< std::shared_ptr< Posterior >>	posteriors,
		const std::vector< std::string >	repeated_par
	)

check the repeated parameters

Parameters

dummy_Nposteriors	number of posterior objects
posteriors	pointers to Posterior objects
repeated_par	repeated parameters

Definition at line 288 of file CombinedPosterior.cpp.

◆ m_set_common_repeated_par()

void cbl::statistics::CombinedPosterior::m_set_common_repeated_par	(	std::vector< std::shared_ptr< Posterior >>	posteriors,
		const bool	is_in_parnames,
		const int	N,
		const int	k,
		const std::vector< std::string >	repeated_par,
		const std::vector< std::vector< std::vector< int >>>	common_repeated_par,
		std::vector< std::shared_ptr< cbl::statistics::PriorDistribution >> &	prior_distributions,
		std::vector< std::string > &	parameter_names,
		std::vector< std::string > &	original_names,
		std::vector< ParameterType > &	parameter_types
	)

set a common repeated parameter

Parameters

posteriors	pointer to the Posterior objects
is_in_parnames	if true, the parameter is already in the vector of parameter names
N	index of the Posterior object
k	index of the parameter of the N-th Posterior
repeated_par	repeated parameter names
common_repeated_par	indices of the common repeated parameters
prior_distributions	vector containing all the Posterior objects
parameter_names	vector containing all the parameter names
original_names	vector of original parameter names
parameter_types	vector containing all the parameter types

Definition at line 358 of file CombinedPosterior.cpp.

◆ m_set_parameters_priors()

void cbl::statistics::CombinedPosterior::m_set_parameters_priors	(	std::vector< std::shared_ptr< Posterior >>	posteriors,
		std::vector< std::string >	repeated_par = `{}`,
		const std::vector< std::vector< std::vector< int >>>	common_repeated_par = `{}`
	)

set the parameters and the priors

Parameters

posteriors	pointers to Posterior objects
repeated_par	parameters shared by different probes, for which the user wants different posteriors for each probe. For example, if the probes A and B depend on the same parameter \(p\), whose identification string is "par", then "par" must be given in input if the user desires to have different posteriors of \(p\) for the two probes A and B. This is useful in the case of astrophysical parameters, e.g. the parameters describing galaxy cluster profiles.
common_repeated_par	for each argument in repeated_par, a vector of vectors of integers can be defined here. Such vectors define the sets of probes for which the same priors and posteriors are provided for the same parameters. For example, let us consider the two sets of probes {A1, A2, A3} and {B1, B2, B3}, provided in the posteriors parameter. All the probes (A1, A2, A3, B1, B2, B3) depend on the parameter \(p\), whose identification string is "par", and we set repeated_par = {"par"}. If we want each pair of probes {A1, B1}, {A2, B2}, {A3, B3}, to provide a different posterior on \(p\), we must set common_repeated_par = { { {0,1}, {2,3}, {4,5} } }. This is useful when different probes in the same bin provide constraints on the same parameters. If common_repeated_par is not provided, every probe depending on \(p\) will provide a different posterior on \(p\). If two parameters are provided in repeated_par, e.g. repeated_par = {"par1", "par2"}, and only "par2" must be shared by more than one probe, then leave blank the vector of vectors corresponding to "par1" in common_repeated_par.

Definition at line 430 of file CombinedPosterior.cpp.

◆ m_set_repeated_par()

void cbl::statistics::CombinedPosterior::m_set_repeated_par	(	std::vector< std::shared_ptr< Posterior >>	posteriors,
		const bool	is_in_parnames,
		const int	N,
		const int	k,
		const std::vector< std::string >	repeated_par,
		const std::vector< std::vector< std::vector< int >>>	common_repeated_par,
		std::vector< std::shared_ptr< cbl::statistics::PriorDistribution >> &	prior_distributions,
		std::vector< std::string > &	parameter_names,
		std::vector< std::string > &	original_names,
		std::vector< ParameterType > &	parameter_types
	)

set a repeated parameter

Parameters

posteriors	pointer to the Posterior objects
is_in_parnames	if true, the parameter is already in the vector of parameter names
N	index of the Posterior object
k	index of the parameter of the N-th Posterior
repeated_par	repeated parameter names
common_repeated_par	indices of the common repeated parameters
prior_distributions	vector containing all the Posterior objects
parameter_names	vector containing all the parameter names
original_names	vector of original parameter names
parameter_types	vector containing all the parameter types

Definition at line 410 of file CombinedPosterior.cpp.

◆ maximize() [1/2]

void cbl::statistics::CombinedPosterior::maximize	(	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`
	)

inline

function that maximizes the posterior, finds the best-fit parameters and store 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	std::vector containing initial values for the posterior maximization
parameter_limits	limits for the parameters
max_iter	the maximum number of iterations
tol	the tolerance in finding convergence
epsilon	the simplex side

Definition at line 663 of file CombinedPosterior.h.

◆ maximize() [2/2]

void cbl::statistics::CombinedPosterior::maximize	(	const std::vector< double >	start,
		const unsigned int	max_iter = `10000`,
		const double	tol = `1.e-6`,
		const double	epsilon = `1.e-4`
	)

function that maximize the posterior, find the best-fit parameters and store them in model

Parameters

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

Definition at line 946 of file CombinedPosterior.cpp.

◆ operator()()

double cbl::statistics::CombinedPosterior::operator() ( std::vector< double > & pp ) const

evaluate the un-normalized posterior as the product of the un-normalized entry posteriors. For N Posterior objects, at a given point \( \vec{\theta_i} \) in the parameter space:

\[ P(\vec{\theta_i} | \vec{d}) = \prod_{j=1}^{N} \mathcal{L_j}(\vec{d}|\vec{\theta_i}) \cdot Pr(\vec{\theta_i}) \]

where \(P\) is the combined posterior, \(\mathcal{L_j}(\vec{d}|\vec{\theta})\) is the j-th likelihood function and \(Pr(\vec{\theta_i})\) is the prior distribution.

Parameters

pp	the parameters

Returns: the value of the un-normalized posterior

Definition at line 885 of file CombinedPosterior.cpp.

◆ read()

std::vector< std::vector< double > > cbl::statistics::CombinedPosterior::read	(	const std::string	path,
		const std::string	filename
	)

read an entire 2d table data (MCMC chain) of unknown dimension

Parameters

path	the path in which the file is stored
filename	the name of the file that has to be read

Returns: two-dimensional vector containing all the read data

Definition at line 1239 of file CombinedPosterior.cpp.

◆ sample_stretch_move()

void cbl::statistics::CombinedPosterior::sample_stretch_move	(	const double	aa = `2`,
		const bool	parallel = `true`,
		const std::string	outputFile = `par::defaultString`,
		const int	start = `0`,
		const int	thin = `1`,
		const int	nbins = `50`
	)

sample the posterior using the stretch-move sampler (Foreman-Mackey et al. 2012)

Parameters

aa	the parameter of the \(g(z)\) distribution
parallel	false \(\rightarrow\) non-parallel sampler; true \(\rightarrow\) parallel sampler
outputFile	output file where the chains are written during run-time. Leave it to default value to have no output. WARNING: this option is intended for debug. It only works for the non-parallelized stretch-move algorithm. The chain in output will be written in a different format with respect to the method cbl::statistics::Posterior::write_chain::ascii col1) chain step col2) walker index col3-npar) parameter values col npar+3) value of the posterior
start	the minimum chain position used to compute the median
thin	the step used for chain dilution
nbins	the number of bins to estimate the posterior distribution, used to assess its properties

Warning: if parallel is set true, than pointers cannot be used inside the posterior function

Definition at line 833 of file CombinedPosterior.cpp.

◆ set_log_posterior()

void cbl::statistics::CombinedPosterior::set_log_posterior	(	const std::vector< double >	logpostA,
		const std::vector< double >	logpostB
	)

set the internal values of m_log_posterior as the concatenation of the logposterior vectors of two cosmological chains

Parameters

logpostA	the first logposterior distribution
logpostB	the second logposterior distribution

Definition at line 641 of file CombinedPosterior.cpp.

◆ set_parameters()

void cbl::statistics::CombinedPosterior::set_parameters	(	const std::vector< std::vector< double >>	parametersA,
		const std::vector< std::vector< double >>	parametersB
	)

set the internal values of m_parameters as the concatenation of the parameters vectors of two cosmological chains

Parameters

parametersA	the first parameters vector
parametersB	the second parameter vector

Definition at line 626 of file CombinedPosterior.cpp.

◆ set_weight()

void cbl::statistics::CombinedPosterior::set_weight	(	const std::vector< double >	weightsA,
		const std::vector< double >	weightsB
	)

set the internal values of m_weight as the concatenation of the weights vectors of two MCMC chains

Parameters

weightsA	the first weights vector
weightsB	the second weights vector

Definition at line 651 of file CombinedPosterior.cpp.

◆ show_results()

void cbl::statistics::CombinedPosterior::show_results	(	const int	start,
		const int	thin,
		const int	nbins = `50`,
		const bool	show_mode = `false`,
		const int	ns = `-1`,
		const int	nb = `-1`
	)

show the results of the MCMC combination on the screen.

In the case of the sum of logPosteriors:

if the covariance matrix has been estimated from a set of mock catalogues, and the input parameters ns (number of samples used to estimate the covariance matrix) and nb (number of data measurements, e.g. the bins of the dataset) are 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

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

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

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).

In the case of importance sampling:

The weighted average of the chains parameters are shown.

Parameters

start	the minimum chain position to be written
thin	the step used for dilution on screen
nbins	the number of bins to estimate the posterior distribution, used to assess its properties
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
nb	number of data measurements, e.g. the bins of the dataset

Definition at line 1007 of file CombinedPosterior.cpp.

◆ write_chain()

void cbl::statistics::CombinedPosterior::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

Warning: column only work for ascii chain file

Definition at line 1059 of file CombinedPosterior.cpp.

◆ write_chain_ascii()

void cbl::statistics::CombinedPosterior::write_chain_ascii	(	const std::string	output_dir,
		const std::string	output_file,
		const int	start = `0`,
		const int	thin = `1`,
		const int	prec = `5`,
		const int	ww = `14`
	)

write the chains obtained after the MCMC sampling on an ascii file

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
prec	decimal precision
ww	number of characters to be used as field width

Definition at line 1071 of file CombinedPosterior.cpp.

◆ write_chain_fits()

void cbl::statistics::CombinedPosterior::write_chain_fits	(	const std::string	output_dir,
		const std::string	output_file,
		const int	start = `0`,
		const int	thin = `1`
	)

write the chains obtained after the MCMC sampling on a FITS file

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

Definition at line 1123 of file CombinedPosterior.cpp.

◆ write_maximization_results()

void cbl::statistics::CombinedPosterior::write_maximization_results	(	const std::string	dir_output,
		const std::string	file
	)

write maximization results on a file

Parameters

dir_output	the output directory
file	the name of the output file to be written

Definition at line 1206 of file CombinedPosterior.cpp.

◆ write_model_from_chain()

void cbl::statistics::CombinedPosterior::write_model_from_chain	(	const std::string	output_dir,
		const std::string	output_file,
		const int	start,
		const int	thin,
		const std::vector< double >	xx = `{}`,
		const std::vector< double >	yy = `{}`
	)

write the model computing 16th, 50th and 84th percentiles from the MCMC

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 on screen
xx	x points where the model is computed. If not provided, the x points set for the MCMC are considered.
yy	y points where the model is computed. If not provided, the y points set for the MCMC are considered.

Definition at line 1174 of file CombinedPosterior.cpp.

◆ write_results()

void cbl::statistics::CombinedPosterior::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`,
		const int	nb = `-1`
	)

store 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 (number of samples used to estimate the covariance matrix) and nb (number of data measurements, e.g. the bins of the dataset) are 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

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

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

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 directory
root_file	the root of the output file to be written
start	the minimum chain position to be written
thin	the step used for dilution on screen
nbins	the number of bins to estimate the posterior distribution, used to assess its properties
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
nb	number of data measurements, e.g. the bins of the dataset

Definition at line 1021 of file CombinedPosterior.cpp.

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

Headers/CombinedPosterior.h
Statistics/CombinedPosterior.cpp

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ CombinedPosterior() [1/2]

◆ CombinedPosterior() [2/2]

Member Function Documentation

◆ importance_sampling() [1/2]

◆ importance_sampling() [2/2]

◆ initialize_chains() [1/3]

◆ initialize_chains() [2/3]

◆ initialize_chains() [3/3]

◆ log()

◆ m_add_prior()

◆ m_check_common_repeated_par()

◆ m_check_repeated_par()

◆ m_set_common_repeated_par()

◆ m_set_parameters_priors()

◆ m_set_repeated_par()

◆ maximize() [1/2]

◆ maximize() [2/2]

◆ operator()()

◆ read()

◆ sample_stretch_move()

◆ set_log_posterior()

◆ set_parameters()

◆ set_weight()

◆ show_results()

◆ write_chain()

◆ write_chain_ascii()

◆ write_chain_fits()

◆ write_maximization_results()

◆ write_model_from_chain()

◆ write_results()