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/

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.

Getting Started

Users can install using pip:

pip install fgivenx

from source:

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

or for those on Arch linux it is available on the AUR

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

pip install pytest pytest-runner pytest-mpl
export MPLBACKEND=Agg
pytest <fgivenx-install-location>

# 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 may find QueueManagerThread errors if 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:

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
• numpy
• scipy

Documentation:

• sphinx
• numpydoc

Tests:

• pytest
• pytest-mpl

Optional extras:

• joblib (parallelisation) [+ pillow on some systems]
• tqdm (progress bars)
• getdist (reading of getdist compatible files)

Documentation

Full Documentation is hosted at ReadTheDocs. To build your own local copy of the documentation you'll need to install sphinx. You can then run:

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:

@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

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')

Plot GetDist chains

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')

Contributing

Want to contribute to fgivenx? Awesome! There are many ways you can contribute via the [GitHub repository](https://github.com/handley-lab/fgivenx), 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.

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