A Bayesian approach to the follow-up of candidate gravitational wave signals

Ground-based gravitational wave laser interferometers (LIGO, GEO-600, Virgo and Tama-300) have now reached high sensitivity and duty cycle. We present a Bayesian evidence-based approach to the search for gravitational waves, in particular aimed at the followup of candidate events generated by the analysis pipeline. We introduce and demonstrate an efficient method to compute the evidence and odds ratio between different models, and illustrate this approach using the specific case of the gravitational wave signal generated during the inspiral phase of binary systems, modelled at the leading quadrupole Newtonian order, in synthetic noise. We show that the method is effective in detecting signals at the detection threshold and it is robust against (some types of) instrumental artefacts. The computational efficiency of this method makes it scalable to the analysis of all the triggers generated by the analysis pipelines to search for coalescing binaries in surveys with ground-based interferometers, and to a whole variety of signal waveforms, characterised by a larger number of parameters.Comment: 9 page

Studying stellar binary systems with the Laser Interferometer Space Antenna using Delayed Rejection Markov chain Monte Carlo methods

Bayesian analysis of LISA data sets based on Markov chain Monte Carlo methods has been shown to be a challenging problem, in part due to the complicated structure of the likelihood function consisting of several isolated local maxima that dramatically reduces the efficiency of the sampling techniques. Here we introduce a new fully Markovian algorithm, a Delayed Rejection Metropolis-Hastings Markov chain Monte Carlo method, to efficiently explore these kind of structures and we demonstrate its performance on selected LISA data sets containing a known number of stellar-mass binary signals embedded in Gaussian stationary noise.Comment: 12 pages, 4 figures, accepted in CQG (GWDAW-13 proceedings

Bayesian coherent analysis of in-spiral gravitational wave signals with a detector network

The present operation of the ground-based network of gravitational-wave laser interferometers in "enhanced" configuration brings the search for gravitational waves into a regime where detection is highly plausible. The development of techniques that allow us to discriminate a signal of astrophysical origin from instrumental artefacts in the interferometer data and to extract the full range of information are some of the primary goals of the current work. Here we report the details of a Bayesian approach to the problem of inference for gravitational wave observations using a network of instruments, for the computation of the Bayes factor between two hypotheses and the evaluation of the marginalised posterior density functions of the unknown model parameters. The numerical algorithm to tackle the notoriously difficult problem of the evaluation of large multi-dimensional integrals is based on a technique known as Nested Sampling, which provides an attractive alternative to more traditional Markov-chain Monte Carlo (MCMC) methods. We discuss the details of the implementation of this algorithm and its performance against a Gaussian model of the background noise, considering the specific case of the signal produced by the in-spiral of binary systems of black holes and/or neutron stars, although the method is completely general and can be applied to other classes of sources. We also demonstrate the utility of this approach by introducing a new coherence test to distinguish between the presence of a coherent signal of astrophysical origin in the data of multiple instruments and the presence of incoherent accidental artefacts, and the effects on the estimation of the source parameters as a function of the number of instruments in the network.Comment: 22 page

A Bayesian parameter estimation approach to pulsar time-of-arrival analysis

The increasing sensitivities of pulsar timing arrays to ultra-low frequency (nHz) gravitational waves promises to achieve direct gravitational wave detection within the next 5-10 years. While there are many parallel efforts being made in the improvement of telescope sensitivity, the detection of stable millisecond pulsars and the improvement of the timing software, there are reasons to believe that the methods used to accurately determine the time-of-arrival (TOA) of pulses from radio pulsars can be improved upon. More specifically, the determination of the uncertainties on these TOAs, which strongly affect the ability to detect GWs through pulsar timing, may be unreliable. We propose two Bayesian methods for the generation of pulsar TOAs starting from pulsar "search-mode" data and pre-folded data. These methods are applied to simulated toy-model examples and in this initial work we focus on the issue of uncertainties in the folding period. The final results of our analysis are expressed in the form of posterior probability distributions on the signal parameters (including the TOA) from a single observation.Comment: 16 pages, 4 figure

Early Advanced LIGO binary neutron-star sky localization and parameter estimation

2015 will see the first observations of Advanced LIGO and the start of the gravitational-wave (GW) advanced-detector era. One of the most promising sources for ground-based GW detectors are binary neutron-star (BNS) coalescences. In order to use any detections for astrophysics, we must understand the capabilities of our parameter-estimation analysis. By simulating the GWs from an astrophysically motivated population of BNSs, we examine the accuracy of parameter inferences in the early advanced-detector era. We find that sky location, which is important for electromagnetic follow-up, can be determined rapidly (~5 s), but that sky areas may be hundreds of square degrees. The degeneracy between component mass and spin means there is significant uncertainty for measurements of the individual masses and spins; however, the chirp mass is well measured (typically better than 0.1%).Comment: 4 pages, 2 figures. Published in the proceedings of Amaldi 1

The effects of LIGO detector noise on a 15-dimensional Markov-chain Monte-Carlo analysis of gravitational-wave signals

Gravitational-wave signals from inspirals of binary compact objects (black holes and neutron stars) are primary targets of the ongoing searches by ground-based gravitational-wave (GW) interferometers (LIGO, Virgo, and GEO-600). We present parameter-estimation results from our Markov-chain Monte-Carlo code SPINspiral on signals from binaries with precessing spins. Two data sets are created by injecting simulated GW signals into either synthetic Gaussian noise or into LIGO detector data. We compute the 15-dimensional probability-density functions (PDFs) for both data sets, as well as for a data set containing LIGO data with a known, loud artefact ("glitch"). We show that the analysis of the signal in detector noise yields accuracies similar to those obtained using simulated Gaussian noise. We also find that while the Markov chains from the glitch do not converge, the PDFs would look consistent with a GW signal present in the data. While our parameter-estimation results are encouraging, further investigations into how to differentiate an actual GW signal from noise are necessary.Comment: 11 pages, 2 figures, NRDA09 proceeding

Towards a generic test of the strong field dynamics of general relativity using compact binary coalescence: Further investigations

In this paper we elaborate on earlier work by the same authors in which a novel Bayesian inference framework for testing the strong-field dynamics of General Relativity using coalescing compact binaries was proposed. Unlike methods that were used previously, our technique addresses the question whether one or more 'testing coefficients' (e.g. in the phase) parameterizing deviations from GR are non-zero, rather than all of them differing from zero at the same time. The framework is well-adapted to a scenario where most sources have low signal-to-noise ratio, and information from multiple sources as seen in multiple detectors can readily be combined. In our previous work, we conjectured that this framework can detect generic deviations from GR that can in principle not be accomodated by our model waveforms, on condition that the change in phase near frequencies where the detectors are the most sensitive is comparable to that induced by simple shifts in the lower-order phase coefficients of more than a few percent ($\sim 5$ radians at 150 Hz). To further support this claim, we perform additional numerical experiments in Gaussian and stationary noise according to the expected Advanced LIGO/Virgo noise curves, and coherently injecting signals into the network whose phasing differs structurally from the predictions of GR, but with the magnitude of the deviation still being small. We find that even then, a violation of GR can be established with good confidence.Comment: 15 pages, 7 figures, Amaldi 9 proceeding

Inference on inspiral signals using LISA MLDC data

In this paper we describe a Bayesian inference framework for analysis of data obtained by LISA. We set up a model for binary inspiral signals as defined for the Mock LISA Data Challenge 1.2 (MLDC), and implemented a Markov chain Monte Carlo (MCMC) algorithm to facilitate exploration and integration of the posterior distribution over the 9-dimensional parameter space. Here we present intermediate results showing how, using this method, information about the 9 parameters can be extracted from the data.Comment: Accepted for publication in Classical and Quantum Gravity, GWDAW-11 special issu

The Mock LISA Data Challenges: from Challenge 3 to Challenge 4

The Mock LISA Data Challenges are a program to demonstrate LISA data-analysis capabilities and to encourage their development. Each round of challenges consists of one or more datasets containing simulated instrument noise and gravitational waves from sources of undisclosed parameters. Participants analyze the datasets and report best-fit solutions for the source parameters. Here we present the results of the third challenge, issued in Apr 2008, which demonstrated the positive recovery of signals from chirping Galactic binaries, from spinning supermassive--black-hole binaries (with optimal SNRs between ~ 10 and 2000), from simultaneous extreme-mass-ratio inspirals (SNRs of 10-50), from cosmic-string-cusp bursts (SNRs of 10-100), and from a relatively loud isotropic background with Omega_gw(f) ~ 10^-11, slightly below the LISA instrument noise.Comment: 12 pages, 2 figures, proceedings of the 8th Edoardo Amaldi Conference on Gravitational Waves, New York, June 21-26, 200

Report on the first round of the Mock LISA Data Challenges

The Mock LISA Data Challenges (MLDCs) have the dual purpose of fostering the development of LISA data analysis tools and capabilities, and demonstrating the technical readiness already achieved by the gravitational-wave community in distilling a rich science payoff from the LISA data output. The first round of MLDCs has just been completed: nine data sets containing simulated gravitational wave signals produced either by galactic binaries or massive black hole binaries embedded in simulated LISA instrumental noise were released in June 2006 with deadline for submission of results at the beginning of December 2006. Ten groups have participated in this first round of challenges. Here we describe the challenges, summarise the results, and provide a first critical assessment of the entries.Comment: Proceedings report from GWDAW 11. Added author, added reference, clarified some text, removed typos. Results unchanged; Removed author, minor edits, reflects submitted versio