=======
pyemcee
=======
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:target: https://doi.org/10.5281/zenodo.4495911
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:target: https://mybinder.org/v2/gh/mcfit/pyemcee/HEAD?labpath=Notebook.ipynb
Description
===========
**pyemcee** is a Python implementation of the *affine-invariant Markov chain Monte Carlo (MCMC) ensemble sampler*, based on `sl_emcee <https://github.com/mcfit/sl_emcee>`_ by `M. A. Nowak <http://space.mit.edu/home/mnowak/isis_vs_xspec/>`_, an S-Lang/`ISIS <http://space.mit.edu/cxc/isis/>`_ implementation of the MCMC Hammer proposed by `Goodman & Weare (2010) <http://dx.doi.org/10.2140/camcos.2010.5.65>`_, and also implemented in Python (`emcee <https://github.com/dfm/emcee>`_) by `Foreman-Mackey et al. (2013) <https://ui.adsabs.harvard.edu/abs/2013PASP..125..306F/abstract>`_.
Installation
============
To install the last version, all you should need to do is
.. code-block::
$ python setup.py install
To install the stable version, you can use the preferred installer program (pip):
.. code-block::
$ pip install pyemcee
or you can install it from the cross-platform package manager *conda*:
.. code-block::
$ conda install -c conda-forge pyemcee
This package requires the following packages:
- `NumPy <https://numpy.org/>`_
- `SciPy <https://scipy.org/scipylib/>`_
- `Matplotlib <https://matplotlib.org/>`_
How to Use
==========
The Documentation of the functions provides in detail in the *API Documentation* (`mcfit.github.io/pyemcee/doc <https://mcfit.github.io/pyemcee/doc>`_). This Python library creates the MCMC sampling for given upper and lower uncertainties, and propagates uncertainties of parameters into the function.
See *Jupyter Notebook*: `Notebook.ipynb <https://github.com/mcfit/pyemcee/blob/master/Notebook.ipynb>`_
Run *Jupyter Notebook* on `Binder <https://mybinder.org/v2/gh/mcfit/pyemcee/HEAD?labpath=Notebook.ipynb>`_:
.. image:: https://mybinder.org/badge_logo.svg
:target: https://mybinder.org/v2/gh/mcfit/pyemcee/HEAD?labpath=Notebook.ipynb
First, you need to load the **pyemcee** library as follows:
.. code-block:: python
import pyemcee
import numpy as np
You need to define your function. For example:
.. code-block:: python
def myfunc21(input1):
result1 = np.sum(input1)
result2 = input1[1] ** input1[0]
return [result1, result2]
Then, specify the upper and lower uncertainties of the prior parameters:
.. code-block:: python
input1 = np.array([1., 2.])
input1_err = np.array([0.2, 0.5])
input1_err_p = input1_err
input1_err_m = -input1_err
output1 = myfunc21(input1)
output1_num = len(output1)
Choose the appropriate uncertainty distribution. For example, for a uniform distribution, use_gaussian=0, and a Gaussian distribution use_gaussian=1. Then, specify the number of walkers and the number of iterations, e.g. walk_num=30 and iteration_num=100. You can then create the MCMC sample and propagate the uncertainties of the input parameters into your defined functions as follows:
.. code-block:: python
use_gaussian=0 # uniform distribution from min value to max value
walk_num=30 # number of walkers
iteration_num=100 # number of samplers
mcmc_sim = pyemcee.hammer(myfunc21, input1, input1_err_m,
input1_err_p, output1, walk_num,
iteration_num, use_gaussian)
To determine the upper and lower errors of the function outputs, you need to run with the chosen appropriate confidence level. For example, a 1.645-sigma standard deviation can be specified with clevel=0.90. For a 1-sigma standard deviation, we have clevel=0.682:
.. code-block:: python
clevel=0.68268949 # 1-sigma
output1_error = pyemcee.find_errors(output1, mcmc_sim, clevel, do_plot=1)
which shows the following distribution histograms:
.. image:: https://raw.githubusercontent.com/mcfit/pyemcee/master/examples/images/histogram0.png
:width: 100
.. image:: https://raw.githubusercontent.com/mcfit/pyemcee/master/examples/images/histogram1.png
:width: 100
To prevent plotting, you should set do_plot=None. To print the results:
.. code-block:: python
for i in range(0, output1_num):
print(output1[i], output1_error[i,:])
which provide the upper and lower limits on each parameter:
.. code-block::
3.0 [-0.35801017 0.35998471]
2.0 [-0.37573196 0.36297235]
For other standard deviation, you should use different confidence levels:
.. code-block:: python
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 pyemcee library, please read the `API Documentation <https://mcfit.github.io/pyemcee/doc>`_ published on `mcfit.github.io/pyemcee <https://mcfit.github.io/pyemcee>`_.
Learn More
==========
================== =============================================
**Documentation** https://pyemcee.readthedocs.io/
**Repository** https://github.com/mcfit/pyemcee
**Issues & Ideas** https://github.com/mcfit/pyemcee/issues
**Conda-Forge** https://anaconda.org/conda-forge/pyemcee
**PyPI** https://pypi.org/project/pyemcee/
**Archive** `10.5281/zenodo.4495911 <https://doi.org/10.5281/zenodo.4495911>`_
================== =============================================
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"description": "=======\npyemcee\n=======\n\n.. image:: https://img.shields.io/pypi/v/pyemcee.svg?style=flat\n :target: https://pypi.python.org/pypi/pyemcee/\n :alt: PyPI Version\n \n.. image:: https://app.travis-ci.com/mcfit/pyemcee.svg?branch=master\n :target: https://app.travis-ci.com/github/mcfit/pyemcee\n :alt: Build Status\n \n.. image:: https://ci.appveyor.com/api/projects/status/oqnksaooj338xn4d?svg=true\n :target: https://ci.appveyor.com/project/danehkar/pyemcee\n :alt: Build Status\n \n.. image:: https://coveralls.io/repos/github/mcfit/pyemcee/badge.svg?\n :target: https://coveralls.io/github/mcfit/pyemcee?branch=master\n :alt: Coverage Status\n \n.. image:: https://img.shields.io/badge/license-GPL-blue.svg\n :target: https://github.com/mcfit/pyemcee/blob/master/LICENSE\n :alt: GitHub license\n \n.. image:: https://img.shields.io/conda/vn/conda-forge/pyemcee.svg\n :target: https://anaconda.org/conda-forge/pyemcee\n :alt: Anaconda Cloud\n \n.. image:: https://readthedocs.org/projects/pyemcee/badge/?version=latest\n :target: https://pyemcee.readthedocs.io/en/latest/?badge=latest\n :alt: Documentation Status\n \n.. image:: https://img.shields.io/badge/python-2.7%2C%203.5-blue.svg\n :alt: Support Python versions 2.7, 3.4 and 3.5\n \n.. image:: https://img.shields.io/badge/DOI-10.5281/zenodo.4495911-blue.svg\n :target: https://doi.org/10.5281/zenodo.4495911\n :alt: Zenodo\n \n.. image:: https://mybinder.org/badge_logo.svg\n :target: https://mybinder.org/v2/gh/mcfit/pyemcee/HEAD?labpath=Notebook.ipynb\n\nDescription\n===========\n\n**pyemcee** is a Python implementation of the *affine-invariant Markov chain Monte Carlo (MCMC) ensemble sampler*, based on `sl_emcee <https://github.com/mcfit/sl_emcee>`_ by `M. A. Nowak <http://space.mit.edu/home/mnowak/isis_vs_xspec/>`_, an S-Lang/`ISIS <http://space.mit.edu/cxc/isis/>`_ implementation of the MCMC Hammer proposed by `Goodman & Weare (2010) <http://dx.doi.org/10.2140/camcos.2010.5.65>`_, and also implemented in Python (`emcee <https://github.com/dfm/emcee>`_) by `Foreman-Mackey et al. (2013) <https://ui.adsabs.harvard.edu/abs/2013PASP..125..306F/abstract>`_. \n\n\nInstallation\n============\n\nTo install the last version, all you should need to do is\n\n.. code-block::\n\n $ python setup.py install\n\nTo install the stable version, you can use the preferred installer program (pip):\n\n.. code-block::\n\n $ pip install pyemcee\n\nor you can install it from the cross-platform package manager *conda*:\n\n.. code-block::\n\n $ conda install -c conda-forge pyemcee\n\nThis package requires the following packages:\n\n - `NumPy <https://numpy.org/>`_\n - `SciPy <https://scipy.org/scipylib/>`_\n - `Matplotlib <https://matplotlib.org/>`_\n\nHow to Use\n==========\n\nThe Documentation of the functions provides in detail in the *API Documentation* (`mcfit.github.io/pyemcee/doc <https://mcfit.github.io/pyemcee/doc>`_). This Python library creates the MCMC sampling for given upper and lower uncertainties, and propagates uncertainties of parameters into the function.\n\nSee *Jupyter Notebook*: `Notebook.ipynb <https://github.com/mcfit/pyemcee/blob/master/Notebook.ipynb>`_\n\nRun *Jupyter Notebook* on `Binder <https://mybinder.org/v2/gh/mcfit/pyemcee/HEAD?labpath=Notebook.ipynb>`_:\n\n.. image:: https://mybinder.org/badge_logo.svg\n :target: https://mybinder.org/v2/gh/mcfit/pyemcee/HEAD?labpath=Notebook.ipynb\n\nFirst, you need to load the **pyemcee** library as follows:\n\n.. code-block:: python\n\n import pyemcee\n import numpy as np\n\nYou need to define your function. For example:\n\n.. code-block:: python\n\n def myfunc21(input1):\n result1 = np.sum(input1)\n result2 = input1[1] ** input1[0]\n return [result1, result2]\n\nThen, specify the upper and lower uncertainties of the prior parameters:\n\n.. code-block:: python\n\n input1 = np.array([1., 2.])\n input1_err = np.array([0.2, 0.5])\n input1_err_p = input1_err\n input1_err_m = -input1_err\n output1 = myfunc21(input1)\n output1_num = len(output1)\n\nChoose the appropriate uncertainty distribution. For example, for a uniform distribution, use_gaussian=0, and a Gaussian distribution use_gaussian=1. Then, specify the number of walkers and the number of iterations, e.g. walk_num=30 and iteration_num=100. You can then create the MCMC sample and propagate the uncertainties of the input parameters into your defined functions as follows:\n\n.. code-block:: python\n\n use_gaussian=0 # uniform distribution from min value to max value\n walk_num=30 # number of walkers\n iteration_num=100 # number of samplers\n mcmc_sim = pyemcee.hammer(myfunc21, input1, input1_err_m, \n input1_err_p, output1, walk_num, \n iteration_num, use_gaussian)\n\nTo determine the upper and lower errors of the function outputs, you need to run with the chosen appropriate confidence level. For example, a 1.645-sigma standard deviation can be specified with clevel=0.90. For a 1-sigma standard deviation, we have clevel=0.682:\n\n.. code-block:: python\n\n clevel=0.68268949 # 1-sigma\n output1_error = pyemcee.find_errors(output1, mcmc_sim, clevel, do_plot=1)\n \nwhich shows the following distribution histograms:\n\n.. image:: https://raw.githubusercontent.com/mcfit/pyemcee/master/examples/images/histogram0.png\n :width: 100\n\n.. image:: https://raw.githubusercontent.com/mcfit/pyemcee/master/examples/images/histogram1.png\n :width: 100\n\nTo prevent plotting, you should set do_plot=None. To print the results:\n\n.. code-block:: python\n\n for i in range(0, output1_num):\n print(output1[i], output1_error[i,:])\n\nwhich provide the upper and lower limits on each parameter:\n\n.. code-block::\n\n 3.0 [-0.35801017 0.35998471]\n 2.0 [-0.37573196 0.36297235]\n\nFor other standard deviation, you should use different confidence levels:\n\n.. code-block:: python\n\n clevel=0.38292492 # 0.5-sigma\n clevel=0.68268949 # 1.0-sigma\n clevel=0.86638560 # 1.5-sigma\n clevel=0.90 # 1.645-sigma\n clevel=0.95 # 1.960-sigma\n clevel=0.95449974 # 2.0-sigma\n clevel=0.98758067 # 2.5-sigma\n clevel=0.99 # 2.575-sigma\n clevel=0.99730020 # 3.0-sigma\n clevel=0.99953474 # 3.5-sigma\n clevel=0.99993666 # 4.0-sigma\n clevel=0.99999320 # 4.5-sigma\n clevel=0.99999943 # 5.0-sigma\n clevel=0.99999996 # 5.5-sigma\n clevel=0.999999998# 6.0-sigma\n\nDocumentation\n=============\n\nFor more information on how to use the API functions from the pyemcee library, please read the `API Documentation <https://mcfit.github.io/pyemcee/doc>`_ published on `mcfit.github.io/pyemcee <https://mcfit.github.io/pyemcee>`_.\n\n\nLearn More\n==========\n\n================== =============================================\n**Documentation** https://pyemcee.readthedocs.io/\n**Repository** https://github.com/mcfit/pyemcee\n**Issues & Ideas** https://github.com/mcfit/pyemcee/issues\n**Conda-Forge** https://anaconda.org/conda-forge/pyemcee\n**PyPI** https://pypi.org/project/pyemcee/\n**Archive** `10.5281/zenodo.4495911 <https://doi.org/10.5281/zenodo.4495911>`_\n================== =============================================\n",
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