Multiple detectors, noise-only#

Here we compare lalpulsar_parameter_estimation_nested with cwinpy in the case of simulated Gaussian noise from multiple detectors (H1, L1 and V1). The parameters being estimated are \(h_0\), \(\phi_0\), \(\psi\) and \(\cos{\iota}\), all with uniform priors.

The script for this comparison, using the dynesty nested sampling algorithm, is shown at the bottom of the page. It produces the following comparison data:

../_images/multi_detector_noise_only_corner.png

Evidence table#
Method	\(\\ln{(Z)}\)	\(\\ln{(Z)}\) noise	\(\\ln{}\) Odds
`lalpulsar_parameter_estimation_nested`	488877.478	488884.731	-7.254±0.084
`cwinpy_pe`	488772.955	488780.019	-7.064±0.143
`cwinpy_pe` (grid)	488772.931		-7.088

Parameter table#
Method	\(h_0\)	\(\\phi_0\) (rad)	\(\\psi\) (rad)	\(\\cos{\\iota}\)
`lalpulsar_parameter_estimation_nested`	6.14±5.08×10^-27	1.33±0.88	0.77±0.45	0.02±0.49
90% credible intervals	[0.31, 16.06]×10^-27	[0.15, 2.94]	[0.09, 1.50]	[-0.80, 0.83]
`cwinpy_pe`	5.95±4.95×10^-27	1.33±0.89	0.79±0.44	0.03±0.49
90% credible intervals	[0.52, 15.77]×10^-27	[0.16, 2.99]	[0.10, 1.50]	[-0.80, 0.85]

Maximum a-posteriori#
Method	\(h_0\)	\(\\phi_0\) (rad)	\(\\psi\) (rad)	\(\\cos{\\iota}\)	\(\\ln{(L)}\) max
`lalpulsar_parameter_estimation_nested`	1.16×10^-26	0.87	0.61	0.01	488885.39
`cwinpy_pe`	1.09×10^-26	0.77	0.61	-0.04	488780.58

Combined K-S test p-value: 0.6819

Maximum Jensen-Shannon divergence: 0.0012

CWInPy version: 1.0.0

bilby version: 2.1.1

#!/usr/bin/env python

"""
Compare cwinpy with lalpulsar_parameter_estimation_nested for noise-only
data for a multiple detectors (H1, L1 and V1).
"""

import os
import subprocess as sp

import h5py
import matplotlib
import numpy as np
from bilby.core.prior import Uniform
from comparitors import comparisons
from lalinference import LALInferenceHDF5PosteriorSamplesDatasetName
from lalinference.io import read_samples
from matplotlib import pyplot as plt
from solar_system_ephemerides.paths import body_ephemeris_path, time_ephemeris_path

from cwinpy import HeterodynedData
from cwinpy.pe import pe
from cwinpy.plot import Plot

matplotlib.use("Agg")

# create a fake pulsar parameter file
parcontent = """\
PSRJ     J0123+3456
RAJ      01:23:45.6789
DECJ     34:56:54.321
F0       567.89
F1       -1.2e-12
PEPOCH   56789
"""

label = "multi_detector_noise_only"
outdir = "outputs"

if not os.path.isdir(outdir):
    os.makedirs(outdir)

# add content to the par file
parfile = os.path.join(outdir, "{}.par".format(label))
with open(parfile, "w") as fp:
    fp.write(parcontent)

# create some fake heterodyned data
detectors = ["H1", "L1", "V1"]  # the detector to use
asd = 1e-24  # noise amplitude spectral density
times = np.linspace(1000000000.0, 1000086340.0, 1440)  # times
het = {}
hetfiles = []
for detector in detectors:
    het[detector] = HeterodynedData(
        times=times, par=parfile, fakeasd=asd, detector=detector
    )

    # output the data
    hetfile = os.path.join(outdir, "{}_{}_data.txt".format(label, detector))
    het[detector].write(hetfile)
    hetfiles.append(hetfile)

# create priors
phi0range = [0.0, np.pi]
psirange = [0.0, np.pi / 2.0]
cosiotarange = [-1.0, 1.0]
h0range = [0.0, 1e-23]

# set prior for lalpulsar_parameter_estimation_nested
priorfile = os.path.join(outdir, "{}_prior.txt".format(label))
priorcontent = """H0 uniform {} {}
PHI0 uniform {} {}
PSI uniform {} {}
COSIOTA uniform {} {}
"""
with open(priorfile, "w") as fp:
    fp.write(priorcontent.format(*(h0range + phi0range + psirange + cosiotarange)))

# set prior for bilby
priors = {}
priors["h0"] = Uniform(h0range[0], h0range[1], "h0", latex_label=r"$h_0$")
priors["phi0"] = Uniform(
    phi0range[0], phi0range[1], "phi0", latex_label=r"$\phi_0$", unit="rad"
)
priors["psi"] = Uniform(
    psirange[0], psirange[1], "psi", latex_label=r"$\psi$", unit="rad"
)
priors["cosiota"] = Uniform(
    cosiotarange[0], cosiotarange[1], "cosiota", latex_label=r"$\cos{\iota}$"
)

# run lalpulsar_parameter_estimation_nested
try:
    execpath = os.environ["CONDA_PREFIX"]
except KeyError:
    raise KeyError(
        "Please work in a conda environment with lalsuite and cwinpy installed"
    )

execpath = os.path.join(execpath, "bin")

lppen = os.path.join(execpath, "lalpulsar_parameter_estimation_nested")
n2p = os.path.join(execpath, "lalinference_nest2pos")

Nlive = 1000  # number of nested sampling live points
Nmcmcinitial = 0  # set to 0 so that prior samples are not resampled

outfile = os.path.join(outdir, "{}_nest.hdf".format(label))

# set ephemeris files
efile = body_ephemeris_path(body="earth", jplde="DE405")
sfile = body_ephemeris_path(body="sun", jplde="DE405")
tfile = time_ephemeris_path(units="TCB")

# set the command line arguments
runcmd = " ".join(
    [
        lppen,
        "--verbose",
        "--input-files",
        ",".join(hetfiles),
        "--detectors",
        ",".join(detectors),
        "--par-file",
        parfile,
        "--prior-file",
        priorfile,
        "--Nlive",
        "{}".format(Nlive),
        "--Nmcmcinitial",
        "{}".format(Nmcmcinitial),
        "--outfile",
        outfile,
        "--ephem-earth",
        str(efile),
        "--ephem-sun",
        str(sfile),
        "--ephem-timecorr",
        str(tfile),
    ]
)

with sp.Popen(
    runcmd,
    stdout=sp.PIPE,
    stderr=sp.PIPE,
    shell=True,
    bufsize=1,
    universal_newlines=True,
) as p:
    for line in p.stderr:
        print(line, end="")

# convert nested samples to posterior samples
outpost = os.path.join(outdir, "{}_post.hdf".format(label))
runcmd = " ".join([n2p, "-p", outpost, outfile])
with sp.Popen(
    runcmd,
    stdout=sp.PIPE,
    stderr=sp.PIPE,
    shell=True,
    bufsize=1,
    universal_newlines=True,
) as p:
    for line in p.stdout:
        print(line, end="")

# get posterior samples
post = read_samples(outpost, tablename=LALInferenceHDF5PosteriorSamplesDatasetName)
lp = len(post["H0"])
postsamples = np.zeros((lp, len(priors)))
for i, p in enumerate(priors.keys()):
    postsamples[:, i] = post[p.upper()]

# get evidence
hdf = h5py.File(outpost, "r")
a = hdf["lalinference"]["lalinference_nest"]
evsig = a.attrs["log_evidence"]
evnoise = a.attrs["log_noise_evidence"]
hdf.close()

# run bilby via the pe interface
runner = pe(
    data_file=hetfiles,
    par_file=parfile,
    prior=priors,
    detector=detectors,
    outdir=outdir,
    label=label,
)

result = runner.result

# evaluate the likelihood on a grid
gridpoints = 30
grid_size = dict()
for p in priors.keys():
    grid_size[p] = np.linspace(
        np.min(result.posterior[p]), np.max(result.posterior[p]), gridpoints
    )

grunner = pe(
    data_file=hetfiles,
    par_file=parfile,
    prior=priors,
    detector=detectors,
    outdir=outdir,
    label=label,
    grid=True,
    grid_kwargs={"grid_size": grid_size},
)

grid = grunner.grid

# output comparisons
comparisons(label, outdir, grid, priors, cred=0.9)

# create results plot
allresults = {
    "lalpulsar_parameter_estimation_nested": outpost,
    "cwinpy_pe": result,
    "cwinpy_pe (grid)": grid,
}

colors = {
    key: plt.rcParams["axes.prop_cycle"].by_key()["color"][i]
    for i, key in enumerate(allresults.keys())
}

plot = Plot(
    results=allresults,
    parameters=list(priors.keys()),
    plottype="corner",
)

plot.plot(
    bins=50,
    smooth=0.9,
    quantiles=[0.16, 0.84],
    levels=(1 - np.exp(-0.5), 1 - np.exp(-2), 1 - np.exp(-9 / 2.0)),
    fill_contours=True,
    colors=colors,
)

plot.savefig(os.path.join(outdir, "{}_corner.png".format(label)), dpi=150)