fgivenx

===================================== fgivenx: Functional Posterior Plotter

:fgivenx: Functional Posterior Plotter :Author: Will Handley :Version: 2.4.2 :Homepage: https://github.com/handley-lab/fgivenx :Documentation: http://fgivenx.readthedocs.io/

.. image:: https://github.com/handley-lab/fgivenx/workflows/CI/badge.svg?branch=master :target: https://github.com/handley-lab/fgivenx/actions?query=workflow%3ACI+branch%3Amaster :alt: Build Status .. image:: https://codecov.io/gh/handley-lab/fgivenx/branch/master/graph/badge.svg :target: https://codecov.io/gh/handley-lab/fgivenx :alt: Test Coverage Status .. image:: https://badge.fury.io/py/fgivenx.svg :target: https://badge.fury.io/py/fgivenx :alt: PyPi location .. image:: https://readthedocs.org/projects/fgivenx/badge/?version=latest :target: https://fgivenx.readthedocs.io/en/latest/?badge=latest :alt: Documentation Status .. image:: http://joss.theoj.org/papers/cf6f8ac309d6a18b6d6cf08b64aa3f62/status.svg :target: http://joss.theoj.org/papers/cf6f8ac309d6a18b6d6cf08b64aa3f62 :alt: Review Status .. image:: https://zenodo.org/badge/100947684.svg :target: https://zenodo.org/badge/latestdoi/100947684 :alt: Permanent DOI .. image:: https://img.shields.io/badge/arXiv-1908.01711-b31b1b.svg :target: https://arxiv.org/abs/1908.01711 :alt: Open-access paper

Description

fgivenx is a python package for plotting posteriors of functions. It is currently used in astronomy, but will be of use to any scientists performing Bayesian analyses which have predictive posteriors that are functions.

This package allows one to plot a predictive posterior of a function, dependent on sampled parameters. We assume one has a Bayesian posterior Post(theta|D,M) described by a set of posterior samples {theta_i}~Post. If there is a function parameterised by theta y=f(x;theta), then this script will produce a contour plot of the conditional posterior P(y|x,D,M) in the (x,y) plane.

The driving routines are fgivenx.plot_contours, fgivenx.plot_lines and fgivenx.plot_dkl. The code is compatible with getdist, and has a loading function provided by fgivenx.samples_from_getdist_chains.

|image0|

Getting Started

Users can install using pip:

.. code:: bash

pip install fgivenx

from source:

.. code:: bash

git clone https://github.com/handley-lab/fgivenx cd fgivenx python setup.py install --user

or for those on Arch linux <https://www.archlinux.org/>__ it is available on the AUR <https://aur.archlinux.org/packages/python-fgivenx/>__

You can check that things are working by running the test suite (You may encounter warnings if the optional dependency joblib is not installed):

.. code:: bash

pip install pytest pytest-runner pytest-mpl export MPLBACKEND=Agg pytest

or, equivalently

git clone https://github.com/handley-lab/fgivenx cd fgivenx python setup.py test

Check the dependencies listed in the next section are installed. You can then use the fgivenx module from your scripts.

Some users of OSX or Anaconda <https://en.wikipedia.org/wiki/Anaconda_(Python_distribution)>__ may find QueueManagerThread errors if Pillow <https://pypi.org/project/Pillow/>__ is not installed (run pip install pillow).

If you want to use parallelisation, have progress bars or getdist compatibility you should install the additional optional dependencies:

.. code:: bash

pip install joblib tqdm getdist

or, equivalently

pip install -r requirements.txt

You may encounter warnings if you don't have the optional dependency joblib installed.

Dependencies

Basic requirements:

• Python 2.7+ or 3.4+
• matplotlib <https://pypi.org/project/matplotlib/>__
• numpy <https://pypi.org/project/numpy/>__
• scipy <https://pypi.org/project/scipy/>__

Documentation:

• sphinx <https://pypi.org/project/Sphinx/>__
• numpydoc <https://pypi.org/project/numpydoc/>__

Tests:

• pytest <https://pypi.org/project/pytest/>__
• pytest-mpl <https://pypi.org/project/pytest-mpl/>__

Optional extras:

• joblib <https://pypi.org/project/joblib/>__ (parallelisation) [+ pillow <https://pypi.org/project/Pillow/>__ on some systems]
• tqdm <https://pypi.org/project/tqdm/>__ (progress bars)
• getdist <https://pypi.org/project/GetDist/>__ (reading of getdist compatible files)

Documentation

Full Documentation is hosted at ReadTheDocs <http://fgivenx.readthedocs.io/>. To build your own local copy of the documentation you'll need to install sphinx <https://pypi.org/project/Sphinx/>. You can then run:

.. code:: bash

cd docs make html

Citation

If you use fgivenx to generate plots for a publication, please cite as: ::

Handley, (2018). fgivenx: A Python package for functional posterior plotting . Journal of Open Source Software, 3(28), 849, https://doi.org/10.21105/joss.00849

or using the BibTeX:

.. code:: bibtex

@article{fgivenx, doi = {10.21105/joss.00849}, url = {http://dx.doi.org/10.21105/joss.00849}, year = {2018}, month = {Aug}, publisher = {The Open Journal}, volume = {3}, number = {28}, author = {Will Handley}, title = {fgivenx: Functional Posterior Plotter}, journal = {The Journal of Open Source Software} }

Example Usage

Plot user-generated samples

.. code:: python

import numpy
import matplotlib.pyplot as plt
from fgivenx import plot_contours, plot_lines, plot_dkl


# Model definitions
# =================
# Define a simple straight line function, parameters theta=(m,c)
def f(x, theta):
    m, c = theta
    return m * x + c


numpy.random.seed(1)

# Posterior samples
nsamples = 1000
ms = numpy.random.normal(loc=-5, scale=1, size=nsamples)
cs = numpy.random.normal(loc=2, scale=1, size=nsamples)
samples = numpy.array([(m, c) for m, c in zip(ms, cs)]).copy()

# Prior samples
ms = numpy.random.normal(loc=0, scale=5, size=nsamples)
cs = numpy.random.normal(loc=0, scale=5, size=nsamples)
prior_samples = numpy.array([(m, c) for m, c in zip(ms, cs)]).copy()

# Set the x range to plot on
xmin, xmax = -2, 2
nx = 100
x = numpy.linspace(xmin, xmax, nx)

# Set the cache
cache = 'cache/test'
prior_cache = cache + '_prior'

# Plotting
# ========
fig, axes = plt.subplots(2, 2)

# Sample plot
# -----------
ax_samples = axes[0, 0]
ax_samples.set_ylabel(r'$c$')
ax_samples.set_xlabel(r'$m$')
ax_samples.plot(prior_samples.T[0], prior_samples.T[1], 'b.')
ax_samples.plot(samples.T[0], samples.T[1], 'r.')

# Line plot
# ---------
ax_lines = axes[0, 1]
ax_lines.set_ylabel(r'$y = m x + c$')
ax_lines.set_xlabel(r'$x$')
plot_lines(f, x, prior_samples, ax_lines, color='b', cache=prior_cache)
plot_lines(f, x, samples, ax_lines, color='r', cache=cache)

# Predictive posterior plot
# -------------------------
ax_fgivenx = axes[1, 1]
ax_fgivenx.set_ylabel(r'$P(y|x)$')
ax_fgivenx.set_xlabel(r'$x$')
cbar = plot_contours(f, x, prior_samples, ax_fgivenx,
                     colors=plt.cm.Blues_r, lines=False,
                     cache=prior_cache)
cbar = plot_contours(f, x, samples, ax_fgivenx, cache=cache)

# DKL plot
# --------
ax_dkl = axes[1, 0]
ax_dkl.set_ylabel(r'$D_\mathrm{KL}$')
ax_dkl.set_xlabel(r'$x$')
ax_dkl.set_ylim(bottom=0, top=2.0)
plot_dkl(f, x, samples, prior_samples, ax_dkl,
         cache=cache, prior_cache=prior_cache)

ax_lines.get_shared_x_axes().join(ax_lines, ax_fgivenx, ax_samples)

fig.tight_layout()
fig.savefig('plot.png')

|image0|

Plot GetDist chains

.. code:: python

import numpy
import matplotlib.pyplot as plt
from fgivenx import plot_contours, samples_from_getdist_chains

file_root = './plik_HM_TT_lowl/base_plikHM_TT_lowl'
samples, weights = samples_from_getdist_chains(['logA', 'ns'], file_root)

def PPS(k, theta):
    logA, ns = theta
    return logA + (ns - 1) * numpy.log(k)
    
k = numpy.logspace(-4,1,100)
cbar = plot_contours(PPS, k, samples, weights=weights)
cbar = plt.colorbar(cbar,ticks=[0,1,2,3])
cbar.set_ticklabels(['',r'$1\sigma$',r'$2\sigma$',r'$3\sigma$'])

plt.xscale('log')
plt.ylim(2,4)
plt.ylabel(r'$\ln\left(10^{10}\mathcal{P}_\mathcal{R}\right)$')
plt.xlabel(r'$k / {\rm Mpc}^{-1}$')
plt.tight_layout()
plt.savefig('planck.png')

|image1|

Contributing

Want to contribute to fgivenx? Awesome! There are many ways you can contribute via the GitHub repository, see below.

Opening issues

Open an issue to report bugs or to propose new features.

Proposing pull requests

Pull requests are very welcome. Note that if you are going to propose drastic changes, be sure to open an issue for discussion first, to make sure that your PR will be accepted before you spend effort coding it.

.. |image0| image:: https://raw.githubusercontent.com/handley-lab/fgivenx/master/plot.png .. |image1| image:: https://raw.githubusercontent.com/handley-lab/fgivenx/master/planck.png

Changelog

:v2.2.0: Paper accepted :v2.1.17: 100% coverage :v2.1.16: Tests fixes :v2.1.15: Additional plot tests :v2.1.13: Further bug fix in test suite for image comparison :v2.1.12: Bug fix in test suite for image comparison :v2.1.11: Documentation upgrades :v2.1.10: Added changelog