fgivenx 2.1.2a

fgivenx: Functional Posterior Plotter

fgivenx: Functional Posterior Plotter

These packages allow one to compute 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 f(x;theta), then this script will produce a contour plot of the conditional posterior P(f|x,D,M) in the (x,f) plane.

The driving routine is fgivenx.compute_contours, and example usage can be found by running help(fgivenx). It is compatible with getdist, and has a loading function provided by fgivenx.samples.samples_from_getdist_chains.

Installation

Users can install using pip:

pip install fgivenx

using the setup.py:

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

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

Documentation

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:

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

Example Usage

import numpy
import matplotlib.pyplot as plt
from fgivenx import compute_samples, compute_pmf, compute_dkl
from fgivenx.plot import plot, plot_lines


# 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()

# Computation
# ===========
# Examine the function over a range of x's
xmin, xmax = -2, 2
nx = 100
x = numpy.linspace(xmin, xmax, nx)

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

# Compute function samples
fsamps = compute_samples(f, x, samples, cache=cache)
prior_fsamps = compute_samples(f, x, prior_samples, cache=prior_cache)

# Compute dkls
dkls = compute_dkl(f, x, samples, prior_samples, cache=cache, parallel=True)

# Compute probability mass function.
y, pmf = compute_pmf(f, x, samples, cache=cache, parallel=True)
y_prior, pmf_prior = compute_pmf(f, x, prior_samples, cache=prior_cache, parallel=True)

# Plotting
# ========
fig, axes = plt.subplots(2, 2)
prior_color = 'b'
posterior_color = 'r'

# 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], color=prior_color, marker='.', linestyle='')
ax_samples.plot(samples.T[0], samples.T[1], color=posterior_color, marker='.', linestyle='')

# Line plot
# ---------
ax_lines = axes[0, 1]
ax_lines.set_ylabel(r'$y = m x + c$')
ax_lines.set_xlabel(r'$x$')
plot_lines(x, prior_fsamps, ax_lines, color=prior_color)
plot_lines(x, fsamps, ax_lines, color=posterior_color)

# Predictive posterior plot
# -------------------------
ax_fgivenx = axes[1, 1]
ax_fgivenx.set_ylabel(r'$P(y|x)$')
ax_fgivenx.set_xlabel(r'$x$')
cbar = plot(x, y_prior, pmf_prior, ax_fgivenx, colors=plt.cm.Blues_r, lines=False)
cbar = plot(x, y, pmf, ax_fgivenx, colors=plt.cm.Reds_r)

# DKL plot
# --------
ax_dkl = axes[1, 0]
ax_dkl.set_ylabel(r'$D_\mathrm{KL}$')
ax_dkl.set_xlabel(r'$x$')
ax_dkl.plot(x, dkls)
ax_dkl.set_ylim(bottom=0)

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

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