38 research outputs found
Taming outliers in pulsar-timing datasets with hierarchical likelihoods and Hamiltonian sampling
Pulsar-timing datasets have been analyzed with great success using
probabilistic treatments based on Gaussian distributions, with applications
ranging from studies of neutron-star structure to tests of general relativity
and searches for nanosecond gravitational waves. As for other applications of
Gaussian distributions, outliers in timing measurements pose a significant
challenge to statistical inference, since they can bias the estimation of
timing and noise parameters, and affect reported parameter uncertainties. We
describe and demonstrate a practical end-to-end approach to perform Bayesian
inference of timing and noise parameters robustly in the presence of outliers,
and to identify these probabilistically. The method is fully consistent (i.e.,
outlier-ness probabilities vary in tune with the posterior distributions of the
timing and noise parameters), and it relies on the efficient sampling of the
hierarchical form of the pulsar-timing likelihood. Such sampling has recently
become possible with a "no-U-turn" Hamiltonian sampler coupled to a highly
customized reparametrization of the likelihood; this code is described
elsewhere, but it is already available online. We recommend our method as a
standard step in the preparation of pulsar-timing-array datasets: even if
statistical inference is not affected, follow-up studies of outlier candidates
can reveal unseen problems in radio observations and timing measurements;
furthermore, confidence in the results of gravitational-wave searches will only
benefit from stringent statistical evidence that datasets are clean and
outlier-free.Comment: 6 pages, 2 figures, RevTeX 4.
An Efficient Approximation to the Likelihood for Gravitational Wave Stochastic Background Detection Using Pulsar Timing Data
Direct detection of gravitational waves by pulsar timing arrays will become
feasible over the next few years. In the low frequency regime ( Hz --
Hz), we expect that a superposition of gravitational waves from many
sources will manifest itself as an isotropic stochastic gravitational wave
background. Currently, a number of techniques exist to detect such a signal;
however, many detection methods are computationally challenging. Here we
introduce an approximation to the full likelihood function for a pulsar timing
array that results in computational savings proportional to the square of the
number of pulsars in the array. Through a series of simulations we show that
the approximate likelihood function reproduces results obtained from the full
likelihood function. We further show, both analytically and through
simulations, that, on average, this approximate likelihood function gives
unbiased parameter estimates for astrophysically realistic stochastic
background amplitudes.Comment: 10 pages, 3 figure
Analysis of the first IPTA Mock Data Challenge by the EPTA timing data analysis working group
This is a summary of the methods we used to analyse the first IPTA Mock Data
Challenge (MDC), and the obtained results. We have used a Bayesian analysis in
the time domain, accelerated using the recently developed ABC-method which
consists of a form of lossy linear data compression. The TOAs were first
processed with Tempo2, where the design matrix was extracted for use in a
subsequent Bayesian analysis. We used different noise models to analyse the
datasets: no red noise, red noise the same for all pulsars, and individual red
noise per pulsar. We sampled from the likelihood with four different samplers:
"emcee", "t-walk", "Metropolis-Hastings", and "pyMultiNest". All but emcee
agreed on the final result, with emcee failing due to artefacts of the
high-dimensionality of the problem. An interesting issue we ran into was that
the prior of all the 36 (red) noise amplitudes strongly affects the results. A
flat prior in the noise amplitude biases the inferred GWB amplitude, whereas a
flat prior in log-amplitude seems to work well. This issue is only apparent
when using a noise model with individually modelled red noise for all pulsars.
Our results for the blind challenges are in good agreement with the injected
values. For the GWB amplitudes we found h_c = 1.03 +/- 0.11 [10^{-14}], h_c =
5.70 +/- 0.35 [10^{-14}], and h_c = 6.91 +/- 1.72 [10^{-15}], and for the GWB
spectral index we found gamma = 4.28 +/- 0.20, gamma = 4.35 +/- 0.09, and gamma
= 3.75 +/- 0.40. We note that for closed challenge 3 there was quite some
covariance between the signal and the red noise: if we constrain the GWB
spectral index to the usual choice of gamma = 13/3, we obtain the estimates:
h_c = 10.0 +/- 0.64 [10^{-15}], h_c = 56.3 +/- 2.42 [10^{-15}], and h_c = 4.83
+/- 0.50 [10^{-15}], with one-sided 2 sigma upper-limits of: h_c <= 10.98
[10^{-15}], h_c <= 60.29 [10^{-15}], and h_c <= 5.65 [10^{-15}].Comment: 10 pages, 5 figure
From bright binaries to bumpy backgrounds: Mapping realistic gravitational wave skies with pulsar-timing arrays
Within the next several years, pulsar-timing array programs will likely usher in the next era of gravitational-wave astronomy through the detection of a stochastic background of nanohertz-frequency gravitational waves, originating from a cosmological population of inspiraling supermassive binary black holes. While the source positions will likely be isotropic to a good approximation, the gravitational-wave angular power distribution will be anisotropic, with the most massive and/or nearby binaries producing signals that may resound above the background. We study such a realistic angular power distribution, developing fast and accurate sky-mapping strategies to localize pixels and extended regions of excess power while simultaneously modeling the background signal from the less massive and more distant ensemble. We find that power anisotropy will be challenging to discriminate from isotropy for realistic gravitational-wave skies, requiring SNR >10 in order to favor anisotropy with 10:1 posterior odds in our case study. Amongst our techniques, modeling the population signal with multiple point sources in addition to an isotropic background provides the most physically motivated and easily interpreted maps, while spherical-harmonic modeling of the square-root power distribution, P(Ω)^(1/2), performs best in discriminating from overall isotropy. Our techniques are modular and easily incorporated into existing pulsar-timing array analysis pipelines
The Need For Speed: Rapid Refitting Techniques for Bayesian Spectral Characterization of the Gravitational Wave Background Using PTAs
Current pulsar timing array (PTA) techniques for characterizing the spectrum
of a nanohertz-frequency stochastic gravitational-wave background (SGWB) begin
at the stage of timing data. This can be slow and memory intensive with
computational scaling that will worsen PTA analysis times as more pulsars and
observations are added. Given recent evidence for a common-spectrum process in
PTA data sets and the need to understand present and future PTA capabilities to
characterize the SGWB through large-scale simulations, we have developed
efficient and rapid approaches that operate on intermediate SGWB analysis
products. These methods refit SGWB spectral models to previously-computed
Bayesian posterior estimations of the timing power spectra. We test our new
methods on simulated PTA data sets and the NANOGrav -year data set, where
in the latter our refit posterior achieves a Hellinger distance from the
current full production-level pipeline that is . Our methods are
-- times faster than the production-level likelihood and scale
sub-linearly as a PTA is expanded with new pulsars or observations. Our methods
also demonstrate that SGWB spectral characterization in PTA data sets is driven
by the longest-timed pulsars with the best-measured power spectral densities
which is not necessarily the case for SGWB detection that is predicated on
correlating many pulsars. Indeed, the common-process spectral properties found
in the NANOGrav -year data set are given by analyzing only the
longest-timed pulsars out of the full pulsar array, and we find that the
``shallowing'' of the common-process power-law model occurs when
gravitational-wave frequencies higher than ~nanohertz are included.
The implementation of our methods is openly available as a software suite to
allow fast and flexible PTA SGWB spectral characterization and model selection.Comment: 19 pages, 12 figures. Submitting to Physical Review
Hyper-efficient model-independent Bayesian method for the analysis of pulsar timing data
A new model independent method is presented for the analysis of pulsar timing
data and the estimation of the spectral properties of an isotropic
gravitational wave background (GWB). We show that by rephrasing the likelihood
we are able to eliminate the most costly aspects of computation normally
associated with this type of data analysis. When applied to the International
Pulsar Timing Array Mock Data Challenge data sets this results in speedups of
approximately 2 to 3 orders of magnitude compared to established methods. We
present three applications of the new likelihood. In the low signal to noise
regime we sample directly from the power spectrum coefficients of the GWB
signal realization. In the high signal to noise regime, where the data can
support a large number of coefficients, we sample from the joint probability
density of the power spectrum coefficients for the individual pulsars and the
GWB signal realization. Critically in both these cases we need make no
assumptions about the form of the power spectrum of the GWB, or the individual
pulsars. Finally we present a method for characterizing the spatial correlation
between pulsars on the sky, making no assumptions about the form of that
correlation, and therefore providing the only truly general Bayesian method of
confirming a GWB detection from pulsar timing data.Comment: 9 pages, 4 figure