Parallel tempered Markov Chain Monte Carlo sampler. More...

#include "sampling/sampler_differential_evolution_deo_tempered_MCMC.h"

Collaboration diagram for sampler_differential_evolution_deo_tempered_MCMC:

Public Member Functions
	sampler_differential_evolution_deo_tempered_MCMC (int seed)
	Class constructor, accepts the integer seed for a random number generator as an argument.

void	run_sampler (likelihood _L, int start_length, int thin, int temp_stride, int chi2_stride, std::string chain_file, std::string lklhd_file, std::string chi2_file, std::string annealing_file, std::vector< double > means, std::vector< double > ranges, std::vector< std::string > var_names, bool continue_flag, int output_precision=6, int verbosity=0, std::vector< double > inverse_temperatures=std::vector< double >(0))
	Function to run the sampler, takes a likelihood object, name of output files, and tuning parameters for the sampler and returns the MCMC chain, likelihoods and chi squared values. More...

double	RndGaussian (double, double, bool)
	Function to generate random numbers with a gaussian distribution.

double	RndUni (double, double)
	Function to generate real valued random numbers in an interval.

int	RndUnint (int, int)
	Function to generate integer valued random numbers in an interval.

void	set_cpu_distribution (int num_replicas, int num_walkers, int num_likelihood)
	Function to set the distribution of processors in different layers of parallelization. More...

void	set_annealing_schedule (int num_rounds, int geometric_increase, double initial_spacing=1.15)
	Function to set the parameters of the tempering schedule. We now use the adaption scheme from Syed 2019. We need the number of adaption rounds to use and the geometric increase factor for the number of rounds in each sample. More...

void	read_initial_ladder (std::string annealing_file)
	Function reads in an annealing.dat file and set the initial ladder for the sampler to the ladder from the final round in the annealing file. More...

void	set_checkpoint (int ckpt_stride, std::string ckpt_file)
	Function to set the checkpoint/restart functionality. More...

void	estimate_bayesian_evidence (std::vector< std::string > file_names, std::vector< double > temperatures, int burn_in)
	Function to estimate the bayesian evidence using the Thermodynamic Integration method. More...

std::vector< double >	find_best_fit (std::string chain_file, std::string lklhd_file)
	Finds the best fit within provided chain file and returns it.

Private Member Functions
double	update_annealing_params (double *beta, double R[])

double	find_beta (Interpolator1D &fLambda, int k, double Lambda, double eps=1e-12, int MAX_ITR=1e8)

Private Attributes
int	_nrounds
	Function that finds the communication barrier of the tempering problem.

int	_b

double	_initial_spacing

int	TNum

int	ChNum

int	LKLHD_Num

int	dim

int	_ckpt_stride

bool	default_cpu_distribution

bool	_no_initial_ladder

std::string	_old_annealing_file

std::string	_ckpt_file

Ran2RNG	_rng

GaussianRandomNumberGenerator< Ran2RNG >	_grng

MPI_Comm	E_COMM

MPI_Comm	T_COMM

MPI_Comm	L_COMM

MPI_Comm	C_COMM

int	E_size

int	E_rank

int	T_size

int	T_rank

int	L_size

int	L_rank

int	C_size

int	C_rank

Detailed Description

Runs parallel tempered differential evolution ensemble sampling Markov Chain Monte Carlo chains to sample the likelihood surface. This routine uses parallel tempering on top of the differential evolution method of Cajo J.F Ter Braak (2006). This implementation closely follows that of B. Nelson et. al (2013) used for analyzing radial velocity observations (RUN DMC code). We also use the DEO tempering and adaption scheme from Syed et. al (2019). Given an object of type likelihood (which encompases the likelihood, priors and chi squared) the sampler explores and samples the likelihood surface over its dependent parameters. It will provide a sampling of the posterior probability distribution. The likelihood and the chi squared evaluated at the sampled points are also provided by the sampler.

Member Function Documentation

void estimate_bayesian_evidence	(	std::vector< std::string >	file_names,
		std::vector< double >	temperatures,
		int	burn_in
	)

Parameters

file_names	Vector of strings holding the names of the likelihood files corresponding to each tempered level.
temperatures	Vector containing the temperature values for the corresponding log-likelihood sample files. The order of temperatures and likelihood file names in their vectors must be the same.
burn_in	Number of burn-in samples to exclude from the analysis.

void read_initial_ladder ( std::string annealing_file )

Parameters

annealing_file is the file containing the annealing information for the run. Namely the round, ladder, and rejection rates.

void run_sampler	(	likelihood	_L,
		int	start_length,
		int	thin,
		int	temp_stride,
		int	chi2_stride,
		std::string	chain_file,
		std::string	lklhd_file,
		std::string	chi2_file,
		std::string	annealing_file,
		std::vector< double >	means,
		std::vector< double >	ranges,
		std::vector< std::string >	var_names,
		bool	continue_flag,
		int	output_precision = `6`,
		int	verbosity = `0`,
		std::vector< double >	inverse_temperatures = `std::vector<double>(0)`
	)

Parameters

_L	An object of class likelihood.
length	Number of steps (stretch moves) taken by the ensemble sampler.
thin	Frequency that output is saved, e.g. if thin=10 then every 10 steps will be saved into the Chain and Lklhd file. Ideally this is set to the autocorrelation time of the sampler, but this is unknown before actually running the problem.
temp_stride	Number of steps between subsequent communication among chains of different temperatures.
chi2_stride	Number of steps between outputting Chi squared values.
chain_file	String variable holding the name of the output MCMC chain file.
lklhd_file	String variable holding the name of the output likelihood file, contains log-likelihood values for each MCMC step.
chi2_file	String variable holding the name of the output chi squared file, contains chi squared values for the MCMC chain.
annealing_file	String variable holding the name of the output file that contains important stats for acceptance rates between tempering levels. Also produces the summary file which appends .summary to the annealing_file string.
means	Vector holding the mean values of parameters used for initializing the MCMC walkers.
ranges	Vector holding the standard deviation of parameters used for initializing the MCMC walkers.
var_names	A vector of strings. It holds the names for each sampled variable. The names are compiled as a header in the "chain_file". If the vector doesn't contain any names the header will not be generated. If the header is present The Themis analysis tools can use it to correctly label the generated diagnostics plots.
continue_flag	Boolean variable. If set to "True" the sampler would use a checkpoint file to resume it's state and continue the run. If the output files exist the new data is appended to the same files. If set to "false" it will start a new chain using the provided "means" and "ranges" variables to initialize the chain. Note in the latter case existing output files will be overwitten by the new ones.
output_precision	Sets the output precision, the number of significant digits used to represent a number in the sampler output files. The defaul precision is 6.
verbosity	If set to one chain files will be produced for all tempering levels, otherwise only the lowest temperature will produce a chain file which is the deisred posterior probability distribution
inverse_temperatures	Optional vector to set the \( \beta=1/T\) used for parallel tempering.

Here is the call graph for this function:

void set_annealing_schedule	(	int	num_rounds,
		int	geometric_increase,
		double	initial_spacing = `1.15`
	)

Parameters

num_rounds is the number of rounds to run

void set_checkpoint	(	int	ckpt_stride,
		std::string	ckpt_file
	)

Parameters

ckpt_stride	Number of steps between writing a new checkpoint.
ckpt_file	String variable holding the name of the output checkpoint file.

void set_cpu_distribution	(	int	num_replicas,
		int	num_walkers,
		int	num_likelihood
	)

Parameters

num_replicas	Integer value ( \( \geq 1 \)). Number of replicas of the monte carlo process, i.e. number of temperatures. If set to one, the sampler will run without tempering.
num_walkers	Number of walkers used by ensemble sampler. This should be at least a few times the dimension of the parameter space.
num_likelihood	number of threads allocated for each likelihood calculation.

The following plot shows how the sampler scales with different number of walkers per MPI process. The green line shows the ideal case of linear scaling where the run time is inversely proportional to the number of MPI processes used. The purple line shows how the sampler scales with the number of MPI processes. As can be seen in the figure the scaling closely follows linear scaling and always remains within \(\%20\) of the ideal linear scaling.

Sampler scaling plot. The green line shows the linear scaling.

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

sampling/sampler_differential_evolution_deo_tempered_MCMC.h
sampling/sampler_differential_evolution_deo_tempered_MCMC.cpp

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Function Documentation