Description

idl_emcee is an Interactive Data Language (IDL)/GNU Data Language (GDL) implementation of the affine-invariant Markov chain Monte Carlo (MCMC) ensemble sampler, based on sl_emcee by M. A. Nowak, an S-Lang/ISIS implementation of the MCMC Hammer proposed by Goodman & Weare (2010), and then implemented in Python (emcee) by Foreman-Mackey et al. (2013).

Installation

• To get this package, you can simply use git command as follows:

git clone --recursive https://github.com/mcfit/idl_emcee.git

• This package does not include any dependent packages in the current version.

How to Use

The Documentation of the IDL functions provides in detail in the API Documentation (mcfit.github.io/idl_emcee/doc). This IDL library creates the MCMC sampling for given upper and lower uncertainties, and propagates uncertainties of parameters into the function.

See Jupyter Notebook: Notebook.ipynb

Run Jupyter Notebook on Binder:

You need to define your function. For example:

function myfunc1, input
  result1 = total(input)
  result2 = input[1]^input[0]
  return, [result1, result2]
end

and use the appropriate confidence level and uncertainty distribution. For example, for a 1.645-sigma standard deviation with a uniform distribution:

clevel=.9; 1.645-sigma
use_gaussian=0 ; uniform distribution from min value to max value

for a 1-sigma standard deviation with a Gaussian distribution:

clevel=0.68268949 ; 1.0-sigma
use_gaussian=1 ; gaussian distribution from min value to max value

and specify the number of walkers and the number of iterations:

walk_num=30
iteration_num=100

Now you provide the given upper and lower uncertainties of the input parameters:

input=[1. , 2.]
input_err=[0.2, 0.5]
input_err_p=input_err
input_err_m=-input_err
output=myfunc1(input)
temp=size(output,/DIMENSIONS)
output_num=temp[0]

You can create the MCMC sample and propagate the uncertainties of the input parameters into your defined functions as follows:

mcmc_sim=emcee_hammer('myfunc1', input, input_err_m, $
                      input_err_p, output, walk_num, $
                      iteration_num, use_gaussian)

To determine the upper and lower errors of the function outputs, you need to run:

output_error=emcee_find_errors(output, mcmc_sim, clevel, do_plot=1)

Alternatively, you could load the emcee object class as follows:

mc=obj_new('emcee')
mcmc_sim=mc->hammer('myfunc1', input, input_err_m, $
                    input_err_p, output, walk_num=walk_num, $
                    iteration_num=iteration_num, $
                    use_gaussian=use_gaussian)
output_error=mc->find_errors(output, mcmc_sim, clevel=clevel, do_plot=1)

which shows the following distribution histograms:

To print the results:

for i=0, output_num-1 do begin
  print, output[i], transpose(output_error[i,*])
endfor

which provide the upper and lower limits on each parameter:

3.00000     -0.35801017      0.35998471
2.00000     -0.37573196      0.36297235

For other standard deviation, you should use different confidence levels:

clevel=0.38292492 ; 0.5-sigma
clevel=0.68268949 ; 1.0-sigma
clevel=0.86638560 ; 1.5-sigma
clevel=0.90       ; 1.645-sigma
clevel=0.95       ; 1.960-sigma
clevel=0.95449974 ; 2.0-sigma
clevel=0.98758067 ; 2.5-sigma
clevel=0.99       ; 2.575-sigma
clevel=0.99730020 ; 3.0-sigma
clevel=0.99953474 ; 3.5-sigma
clevel=0.99993666 ; 4.0-sigma
clevel=0.99999320 ; 4.5-sigma
clevel=0.99999943 ; 5.0-sigma
clevel=0.99999996 ; 5.5-sigma
clevel=0.999999998; 6.0-sigma

Documentation

For more information on how to use the API functions from the idl_emcee libray, please read the API Documentation published on mcfit.github.io/idl_emcee.

Learn More

Documentation	https://mcfit.github.io/idl_emcee/doc/
Repository	https://github.com/mcfit/idl_emcee
Issues & Ideas	https://github.com/mcfit/idl_emcee/issues
Archive	10.5281/zenodo.4495897