#include "Headers/Posterior.h"

Inheritance diagram for cbl::statistics::Posterior:

Collaboration diagram for cbl::statistics::Posterior:

Public Member Functions
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...

Constructors/destructors
	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

Protected Member Functions
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
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 Posterior.

This class is used to define the distribution

Examples: fit.cpp.

Definition at line 55 of file Posterior.h.

Constructor & Destructor Documentation

◆ Posterior() [1/3]

cbl::statistics::Posterior::Posterior	(	const std::vector< std::shared_ptr< PriorDistribution >>	prior_distributions,
		const Likelihood &	likelihood,
		const int	seed = `5341`
	)

constructor

Parameters

prior_distributions	vector containing the priors for the likelihood parameters
likelihood	pointer to an object of type Likelihood
seed	general seed for prior/posterior distribution and sampler

Definition at line 67 of file Posterior.cpp.

◆ Posterior() [2/3]

cbl::statistics::Posterior::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

Parameters

prior_distributions	vector containing the priors for the likelihood parameters
data	object of type data
model	object of type model
likelihood_type	type of the likelihood
x_index	index(s) of the extra info std::vector containing the point(s) where the model is evaluated
w_index	std::vector containing the data point weight
seed	general seed for prior/posterior distribution and sampler

Definition at line 58 of file Posterior.cpp.

◆ Posterior() [3/3]

cbl::statistics::Posterior::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

Parameters

file_name	the name of the input file
path_file	the path of the input file
parameter_names	the vector containing the names of parameters
usecols	the columns to read
skip_header	the number of lines to skip

Definition at line 84 of file Posterior.cpp.

Member Function Documentation

◆ chi2()

double cbl::statistics::Posterior::chi2 ( const std::vector< double > parameter = {} ) const

the \(\chi^2\)

this function computes

\[ \chi^2 \equiv -2\log(\frac{P(\vec{\theta} | \vec{d})}{Pr(\vec{\theta})}) \]

where \(P(\vec{\theta} | \vec{d})\) is the posterior and \(Pr(\vec{\theta})\) is the prior

Parameters

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

Returns: \(\chi^2\)

Definition at line 155 of file Posterior.cpp.

◆ get_log_posterior()

std::vector<double> cbl::statistics::Posterior::get_log_posterior ( )

inline

get the values of the internal variable m_log_posterior

Returns: vector of double containing the logPosterior for each MCMC step

Definition at line 334 of file Posterior.h.

◆ get_m_likelihood_function()

Likelihood_function cbl::statistics::Posterior::get_m_likelihood_function ( )

inline

get the values of the internal variable m_likelihood_function

Returns: m_likelihood_function

Definition at line 362 of file Posterior.h.

◆ get_m_likelihood_function_grid()

Likelihood_function cbl::statistics::Posterior::get_m_likelihood_function_grid ( )

inline

get the values of the internal variable m_likelihood_function_grid

Returns: m_likelihood_function_grid

Definition at line 369 of file Posterior.h.

◆ get_m_likelihood_inputs()

std::shared_ptr<void> cbl::statistics::Posterior::get_m_likelihood_inputs ( )

inline

get the values of the internal variable m_likelihood_inputs

Returns: pointer containing m_likelihood_inputs

Definition at line 341 of file Posterior.h.

◆ get_m_log_likelihood_function()

LogLikelihood_function cbl::statistics::Posterior::get_m_log_likelihood_function ( )

inline

get the values of the internal variable m_log_likelihood_function

Returns: m_log_likelihood_function

Definition at line 355 of file Posterior.h.

◆ get_m_log_likelihood_function_grid()

LogLikelihood_function cbl::statistics::Posterior::get_m_log_likelihood_function_grid ( )

inline

get the values of the internal variable m_log_likelihood_function_grid

Returns: m_log_likelihood_function_grid

Definition at line 376 of file Posterior.h.

◆ get_m_prior()

std::shared_ptr<cbl::statistics::Prior> cbl::statistics::Posterior::get_m_prior ( )

inline

get the values of the internal variable m_prior

Returns: pointer containing the prior

Definition at line 348 of file Posterior.h.

◆ get_m_use_grid()

bool cbl::statistics::Posterior::get_m_use_grid ( )

inline

get the value of the internal variable m_use_grid

Returns: the boolean value of m_use_grid

Definition at line 320 of file Posterior.h.

◆ get_Nparameters()

int cbl::statistics::Posterior::get_Nparameters ( )

inline

get the number of parameters used

Returns: the value of the internal variable m_Nparameters

Definition at line 306 of file Posterior.h.

◆ get_parameters()

std::vector<std::vector<double> > cbl::statistics::Posterior::get_parameters ( )

inline

get the values of the internal variable m_parameters

Returns: vector of vector containing parameters for each MCMC step

Definition at line 327 of file Posterior.h.

◆ get_response_function()

std::shared_ptr<statistics::Model> cbl::statistics::Posterior::get_response_function ( )

inline

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

Returns: pointer to the response function

Definition at line 392 of file Posterior.h.

◆ importance_sampling()

void cbl::statistics::Posterior::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

Importance sampling is a convenient technique to join independet datasets.

This function takes in input a chain and computes the 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.

It's possible either to sum or overwrite the log likelihood.

Parameters

input_dir	the input directory
input_file	the input file
column	the column 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
n_walkers	this parameter is used here only to parallelize the computation

Warning: column is used only for ASCII chain files

Definition at line 312 of file Posterior.cpp.

◆ initialize_chains() [1/5]

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

initialize 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
n_walkers	the number of parallel chains

Definition at line 615 of file Posterior.cpp.

◆ initialize_chains() [2/5]

void cbl::statistics::Posterior::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 625 of file Posterior.cpp.

◆ initialize_chains() [3/5]

void cbl::statistics::Posterior::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

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
n_walkers	the number of parallel chains
input_dir	the input directory
input_file	the input file

Definition at line 661 of file Posterior.cpp.

◆ initialize_chains() [4/5]

void cbl::statistics::Posterior::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

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

Parameters

chain_size	the chain lenght
n_walkers	the number of parallel chains
value	vector containing the input values, centres of the ball in the parameter space
radius	radius of the ball in the parameter space

Definition at line 637 of file Posterior.cpp.

◆ initialize_chains() [5/5]

void cbl::statistics::Posterior::initialize_chains	(	const int	chain_size,
		const std::vector< std::vector< double >>	chain_value
	)

initialize 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	matrix of size (n_walkers, n_parameters), starting values of the chain

Definition at line 647 of file Posterior.cpp.

◆ log()

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

the logarithm of the un-normalized posterior

\[ P(\vec{\theta} | \vec{d}) = \mathcal{L}(\vec{d}|\vec{\theta}) \cdot Pr(\vec{\theta}) \]

where \(P(\vec{\theta} | \vec{d})\) is the posterior, \(\mathcal{L}(\vec{d}|\vec{\theta})\) is the likelihood, \(Pr(\vec{\theta})\) is the prior, \(\vec{\theta}\) is the set of model parameters and \(\vec{d}\) is the dataset

Parameters

pp	the parameters

Returns: the logarithm of the un-normalized posterior

Definition at line 137 of file Posterior.cpp.

◆ m_generate_seed()

int cbl::statistics::Posterior::m_generate_seed ( )

inlineprotected

generate a seed

Returns: a seed generated from m_seed_generator

Definition at line 104 of file Posterior.h.

◆ m_get_seed()

int cbl::statistics::Posterior::m_get_seed ( )

inline

get the value of the internal variable m_seed

Returns: the value of the internal variable m_seed

Definition at line 313 of file Posterior.h.

◆ m_set_seed()

void cbl::statistics::Posterior::m_set_seed ( const int seed )

protected

set the internal attribute m_seed and related quantities

Parameters

seed the seed

Definition at line 47 of file Posterior.cpp.

◆ maximize() [1/2]

void cbl::statistics::Posterior::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 428 of file Posterior.h.

◆ maximize() [2/2]

void cbl::statistics::Posterior::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 212 of file Posterior.cpp.

◆ operator()()

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

the un-normalized posterior

\[ P((\vec{\theta} | \vec{d}) = \mathcal{L}(\vec{d}|\vec{\theta}) \cdot Pr(\vec{\theta}) \]

where \(P\) is the posterior, \(\mathcal{L}(\vec{d}|\vec{\theta})\) is the likelihood and \(Pr(\vec{\theta})\) is the prior

Parameters

pp	the parameters

Returns: the value of the un-normalized posterior

Definition at line 105 of file Posterior.cpp.

◆ parameters()

std::shared_ptr<ModelParameters> cbl::statistics::Posterior::parameters ( ) const

inline

return the posterior parameters

Returns: pointer containing the posterior parameters

Definition at line 197 of file Posterior.h.

◆ read_chain()

void cbl::statistics::Posterior::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

Parameters

input_dir	the input directory
input_file	the input file
n_walkers	the number of parallel chains
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

Definition at line 361 of file Posterior.cpp.

◆ read_chain_ascii()

void cbl::statistics::Posterior::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

Parameters

input_dir	the intput directory
input_file	the intput file
n_walkers	the number of parallel chains
column	the columns of the input file to be read.
header_lines_to_skip	the lines to be skipped in the chain file

Definition at line 373 of file Posterior.cpp.

◆ read_chain_fits()

void cbl::statistics::Posterior::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

Parameters

input_dir	the input directory
input_file	the input file
n_walkers	the number of parallel chains
column	the columns of the input file to be read

Definition at line 446 of file Posterior.cpp.

◆ sample_stretch_move()

void cbl::statistics::Posterior::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 268 of file Posterior.cpp.

◆ set()

void cbl::statistics::Posterior::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

Parameters

prior_distributions	vector containing the priors for the likelihood parameters
data	pointer to an object of type Data
model	pointer to an object of type model
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	std::vector containing the data point weight
seed	the seed

Definition at line 190 of file Posterior.cpp.

◆ set_model()

void cbl::statistics::Posterior::set_model	(	std::shared_ptr< Model >	model = `NULL`,
		const std::shared_ptr< ModelParameters >	model_parameters = `NULL`
	)

set the model for the posterior analysis

Parameters

model	pointer to the model
model_parameters	parameters of the model

Definition at line 166 of file Posterior.cpp.

◆ set_response_function()

void cbl::statistics::Posterior::set_response_function ( std::shared_ptr< statistics::Model > response )

inline

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

Parameters

response pointer to the response statistics::Model object

Definition at line 384 of file Posterior.h.

◆ show_results()

void cbl::statistics::Posterior::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

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

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 732 of file Posterior.cpp.

◆ weight()

vector< double > cbl::statistics::Posterior::weight	(	const int	start = `0`,
		const int	thin = `1`
	)		const

return the internal member m_weights

Parameters

start	the minimum chain position to be written
thin	the step used for dilution

Returns: vector containing the posterior weights

Definition at line 120 of file Posterior.cpp.

◆ write_chain()

void cbl::statistics::Posterior::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 490 of file Posterior.cpp.

◆ write_chain_ascii()

void cbl::statistics::Posterior::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 502 of file Posterior.cpp.

◆ write_chain_fits()

void cbl::statistics::Posterior::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 560 of file Posterior.cpp.

◆ write_maximization_results()

void cbl::statistics::Posterior::write_maximization_results	(	const std::string	output_dir,
		const std::string	root_file
	)

write maximization results on a file

Parameters

output_dir	the output directory
root_file	the root of the output file to be written

Definition at line 699 of file Posterior.cpp.

◆ write_model_from_chain()

void cbl::statistics::Posterior::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

Parameters

output_dir	the output directory
output_file	the output file
xx	vector of points at which the model is computed
yy	vector of points at which the model is computed
start	the minimum chain position to be written
thin	the step used for dilution on screen

Definition at line 753 of file Posterior.cpp.

◆ write_results()

void cbl::statistics::Posterior::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 741 of file Posterior.cpp.

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

Headers/Posterior.h
Statistics/Posterior.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Posterior() [1/3]

◆ Posterior() [2/3]

◆ Posterior() [3/3]

Member Function Documentation

◆ chi2()

◆ get_log_posterior()

◆ get_m_likelihood_function()

◆ get_m_likelihood_function_grid()

◆ get_m_likelihood_inputs()

◆ get_m_log_likelihood_function()

◆ get_m_log_likelihood_function_grid()

◆ get_m_prior()

◆ get_m_use_grid()

◆ get_Nparameters()

◆ get_parameters()

◆ get_response_function()

◆ importance_sampling()

◆ initialize_chains() [1/5]

◆ initialize_chains() [2/5]

◆ initialize_chains() [3/5]

◆ initialize_chains() [4/5]

◆ initialize_chains() [5/5]

◆ log()

◆ m_generate_seed()

◆ m_get_seed()

◆ m_set_seed()

◆ maximize() [1/2]

◆ maximize() [2/2]

◆ operator()()

◆ parameters()

◆ read_chain()

◆ read_chain_ascii()

◆ read_chain_fits()

◆ sample_stretch_move()

◆ set()

◆ set_model()

◆ set_response_function()

◆ show_results()

◆ weight()

◆ write_chain()

◆ write_chain_ascii()

◆ write_chain_fits()

◆ write_maximization_results()

◆ write_model_from_chain()

◆ write_results()