The data analysis problem of coherently searching for unmodeled gravitational-wave bursts in the data generated by a global network of gravitational-wave observatories has been at the center of research for almost two decades. As data from these detectors is starting to be analyzed, a renewed interest in this problem has been sparked. A Bayesian approach to the problem of coherently searching for gravitational wave bursts with a network of ground-based interferometers is here presented. We demonstrate how to systematically incorporate prior information on the burst signal and its source into the analysis. This information may range from the very minimal, such as best-guess durations, bandwidths, or polarization content, to complete prior knowledge of the signal waveforms and the distribution of sources through spacetime. We show that this comprehensive Bayesian formulation contains several previously proposed detection statistics as special limiting cases, and demonstrate that it outperforms them.
An analytic model a la Middleton of the impulsive noise component in the data of interferometric gravitational wave detectors is proposed, based on an atomic representation of glitches. A fully analytic characterization of the coherent network data analysis algorithm proposed by Rakhmanov and Klimenko is obtained, for the simplest relevant case of triggered detection of unmodeled gravitational wave bursts, using the above noise model. The detector's performance is evaluated under a suitable central-limit hypothesis, and the effects of both the noisiness of the pseudo-templates, and the presenc…
We present a null-stream-based Bayesian unmodeled framework to probe generic gravitational-wave polarizations. Generic metric theories allow six gravitational-wave polarization states, but general relativity only permits the existence of two of them namely the tensorial polarizations. The strain signal measured by an interferometer is a linear combination of the polarization modes and such a linear combination depends on the geometry of the detector and the source location. The detector network of Advanced LIGO and Advanced Virgo allows us to measure different linear combinations of the polari…
The searches of impulsive gravitational waves (GW) in the data of the ground-based interferometers focus essentially on two types of waveforms: short unmodeled bursts and chirps from inspiralling compact binaries. There is room for other types of searches based on different models. Our objective is to fill this gap. More specifically, we are interested in GW chirps with an arbitrary phase/frequency vs. time evolution. These unmodeled GW chirps may be considered as the generic signature of orbiting/spinning sources. We expect quasi-periodic nature of the waveform to be preserved independent of …
The Laser Interferometer Space Antenna (LISA) will open a rich discovery space in the milli-Hertz gravitational wave band. In addition to the anticipated signals from many millions of binary systems, this band may contain new and previously un-imagined sources for which we currently have no models. To detect unmodeled and unexpected signals we need to be able to separate them from instrumental noise artifacts, or glitches. Glitches are a regular feature in the data from ground based laser interferometers, and they were also seen in data from the LISA Pathfinder mission. In contrast to the situ…
We present two search algorithms that implement logarithmic tiling of the time-frequency plane in order to efficiently detect astrophysically unmodeled bursts of gravitational radiation. The first is a straightforward application of the dyadic wavelet transform. The second is a modification of the windowed Fourier transform which tiles the time-frequency plane for a specific Q. In addition, we also demonstrate adaptive whitening by linear prediction, which greatly simplifies our statistical analysis. This is a methodology paper that aims to describe the techniques for identifying significant e…
A Bayesian treatment of the problem of detecting an unmodelled gravitational wave burst with a global network of gravitational wave observatories reveals that several previously proposed statistics have implicit biases that render them sub-optimal for realistic signal populations.
Monte-Carlo simulations are used in the gravitational wave burst detection community to demonstrate and compare the properties of different search techniques. We note that every Monte-Carlo simulation has a corresponding optimal search technique according to both the non-Bayesian Neyman-Pearson criterion and the Bayesian approach, and that this optimal search technique is the Bayesian statistic. When practical, we recommend deriving the optimal statistic for a credible Monte-Carlo simulation, rather than testing ad hoc statistics against that simulation.
A variety of gravitational-wave transient sources can be modeled in the Fourier domain using a power law. This simple power-law model provides a reasonable approximation for gravitational-wave bursts from cosmic string cusps, cosmic string kinks, and the memory effect. Each of these sources is described using a different spectral index. In this work, we simulate interferometer strain data with injections of power-law and memory bursts to demonstrate parameter estimation, signal detection, and model selection. We show how Bayesian inference can be used to measure the power-law spectral index, t…
We present results from an all-sky search for unmodeled gravitational-wave bursts in the data collected by the LIGO, GEO 600 and Virgo detectors between November 2006 and October 2007. The search is performed by three different analysis algorithms over the frequency band 50-6000 Hz. Data are analyzed for times with at least two of the four LIGO-Virgo detectors in coincident operation, with a total live time of 266 days. No events produced by the search algorithms survive the selection cuts. We set a frequentist upper limit on the rate of gravitational-wave bursts impinging on our network of de…
We perform a search for gravitational wave bursts using data from the second science run of the LIGO detectors, using a method based on a wavelet time-frequency decomposition. This search is sensitive to bursts of duration much less than a second and with frequency content in the 100-1100Hz range. It features significant improvements in the instrument sensitivity and in the analysis pipeline with respect to the burst search previously reported by LIGO. Improvements in the search method allow exploring weaker signals, relative to the detector noise floor, while maintaining a low false alarm rat…
Detection of gravitational waves (GW) from highly eccentric binary black hole (BBH) systems can provide insight into their dynamics and formation. To date, all of the LIGO-Virgo BBH detections have been made using quasi-circular templates in their initial discovery. However, recent studies have found some of these systems to be compatible with high eccentricity in the LIGO band, $e_{10 \textrm{Hz}} > 0.1$, possibly pointing to a population of sources that are challenging to detect. Current low-latency search methods used with ground-based GW detector data are not well equipped to detect highly…
We examine the properties of an excess power method to detect gravitational waves in interferometric detector data. This method is designed to detect short-duration (< 0.5 s) burst signals of unknown waveform, such as those from supernovae or black hole mergers. If only the bursts' duration and frequency band are known, the method is an optimal detection strategy in both Bayesian and frequentist senses. It consists of summing the data power over the known time interval and frequency band of the burst. If the detector noise is stationary and Gaussian, this sum is distributed as a chi-squared (n…
Gravitational wave burst is a catch-all category for signals whose durations are shorter than the observation period. We apply a method new to gravitational wave data analysis --- Bayesian non-parameterics --- to the problem of gravitational wave detection, with an emphasis on pulsar timing array observations. In Bayesian non-parametrics, constraints are set on the function space that may be reasonably thought to characterize the range of gravitational-wave signals. This differs from the approaches currently employed or proposed, which focus on introducing parametric signal models or looking f…
We consider the problem of characterisation of burst sources detected with the Laser Interferometer Space Antenna (LISA) using the multi-modal nested sampling algorithm, MultiNest. We use MultiNest as a tool to search for modelled bursts from cosmic string cusps, and compute the Bayesian evidence associated with the cosmic string model. As an alternative burst model, we consider sine-Gaussian burst signals, and show how the evidence ratio can be used to choose between these two alternatives. We present results from an application of MultiNest to the last round of the Mock LISA Data Challenge, …
LISA Pathfinder (LPF), ESA's precursor mission to a gravitational wave observatory, will measure the degree to which two test-masses can be put into free-fall, aiming to demonstrate a residual relative acceleration with a power spectral density (PSD) below 30 fm/s$^2$/Hz$^{1/2}$ around 1 mHz. In LPF data analysis, the measured relative acceleration data series must be fit to other various measured time series data. This fitting is required in different experiments, from system identification of the test mass and satellite dynamics to the subtraction of noise contributions from measured known d…
We investigate the detectability of massive mode of polarization of Gravitational Waves (GWs) in f(R) theory of gravity associated with Gamma Ray Bursts (GRBs) sources. We obtain the beam pattern function of Laser Interferometric Gravitational wave Observatory (LIGO) corresponding to the massive polarization of GWs and perform Bayesian analysis to study this polarization. It is found that the massive polarization component with a mass of 10^-22eV/c2 is too weak to be detected at LIGO with its current configuration.
The nanohertz frequency band explored by pulsar timing arrays provides a unique discovery space for gravitational wave signals. In addition to signals from anticipated sources, such as those from supermassive black hole binaries, some previously unimagined sources may emit transient gravitational waves (a.k.a. bursts) with unknown morphology. Unmodeled transients are not currently searched for in this frequency band, and they require different techniques from those currently employed. Possible sources of such gravitational wave bursts in the nanohertz regime are parabolic encounters of superma…
The LIGO-Virgo collaboration uses a variety of techniques to detect and characterize gravitational waves. One approach is to use templates - models for the signals derived from Einstein's equations. Another approach is to extract the signals directly from the coherent response of the detectors in LIGO-Virgo network. Both approaches played an important role in the first gravitational wave detections. Here we extend the BayesWave analysis algorithm, which reconstructs gravitational wave signals using a collection of continuous wavelets, to use a generalized wavelet family, known as chirplets, th…
Presented in this paper is a technique that we propose for extracting the physical parameters of a rotating stellar core collapse from the observation of the associated gravitational wave signal from the collapse and core bounce. Data from interferometric gravitational wave detectors can be used to provide information on the mass of the progenitor model, precollapse rotation and the nuclear equation of state. We use waveform libraries provided by the latest numerical simulations of rotating stellar core collapse models in general relativity, and from them create an orthogonal set of eigenvecto…
A central challenge in Gravitational Wave Astronomy is identifying weak signals in the presence of non-stationary and non-Gaussian noise. The separation of gravitational wave signals from noise requires good models for both. When accurate signal models are available, such as for binary Neutron star systems, it is possible to make robust detection statements even when the noise is poorly understood. In contrast, searches for "un-modeled" transient signals are strongly impacted by the methods used to characterize the noise. Here we take a Bayesian approach and introduce a multi-component, variab…
A hypothetical photon mass, $m_γ$, gives an energy-dependent light speed in a Lorentz-invariant theory. Such a modification causes an additional time delay between photons of different energies when they travel through a fixed distance. Fast radio bursts (FRBs), with their short time duration and cosmological propagation distance, are excellent astrophysical objects to constrain $m_γ$. Here for the first time we develop a Bayesian framework to study this problem with a catalog of FRBs. Those FRBs with and without redshift measurement are both useful in this framework, and can be combined in a …
A network of observable, macroscopic cosmic (super-)strings may have formed in the early universe. If so, the cusps that generically develop on cosmic-string loops emit bursts of gravitational radiation that could be detectable by both ground- and space-based gravitational-wave interferometers. Here we report on two versions of a LISA-oriented string-burst search pipeline that we have developed and tested within the context of the Mock LISA Data Challenges. The two versions rely on the publicly available MultiNest and PyMC software packages, respectively. To reduce the effective dimensionality…
I explore the possibility of resurrecting an old, non-Bayesian computational approach for inferring the source direction of a gravitational wave from the output of a two-detector network. The method gives the beam pattern response functions and time delay, and performs well even in the presence of noise and unexpected signal forms. I further suggest an improvement to this method in the form of a weighting algorithm that usefully improves its accuracy beyond what can be achieved with simple best-fit methods, validating the new procedure with several small-scale simulations. The approach is iden…
As second-generation gravitational-wave detectors prepare to analyze data at unprecedented sensitivity, there is great interest in searches for unmodeled transients, commonly called bursts. Significant effort has yielded a variety of techniques to identify and characterize such transient signals, and many of these methods have been applied to produce astrophysical results using data from first-generation detectors. However, the computational cost of background estimation remains a challenging problem; it is difficult to claim a 5σ detection with reasonable computational resources without payin…
We calibrate the distance and reconstruct the Hubble diagram of gamma-ray bursts (GRBs) using deep learning. We construct an artificial neural network, which combines the recurrent neural network and Bayesian neural network, and train the network using the Pantheon compilation of type-Ia supernovae. The trained network is used to calibrate the distance of 174 GRBs based on the Combo-relation. We verify that there is no evident redshift evolution of Combo-relation, and obtain the slope and intercept parameters, $γ=0.856^{+0.083}_{-0.078}$ and $\log A=49.661^{+0.199}_{-0.217}$, with an intrinsic…
We consider the issue of reporting the result of search experiment in the most unbiased and efficient way, i.e. in a way which allows an easy interpretation and combination of results and which do not depend on whether the experimenters believe or not to having found the searched-for effect. Since this work uses the language of Bayesian theory, to which most physicists are not used, we find that it could be useful to practitioners to have in a single paper a simple presentation of Bayesian inference, together with an example of application of it in search of rare processes.
Progenitors of short gamma-ray bursts are thought to be neutron stars coalescing with their companion black hole or neutron star, which are one of the main gravitational wave sources. We have devised a Bayesian framework for combining gamma-ray burst and gravitational wave information that allows us to probe short gamma-ray burst luminosities. We show that combined short gamma-ray burst and gravitational wave observations not only improve progenitor distance and inclination angle estimates, they also allow the isotropic luminosities of short gamma-ray bursts to be determined without the need f…
We analyzed the available LIGO data coincident with GRB 070201, a short duration hard spectrum gamma-ray burst whose electromagnetically determined sky position is coincident with the spiral arms of the Andromeda galaxy (M31). Possible progenitors of such short hard GRBs include mergers of neutron stars or a neutron star and black hole, or soft gamma-ray repeater (SGR) flares. These events can be accompanied by gravitational-wave emission. No plausible gravitational wave candidates were found within a 180 s long window around the time of GRB 070201. This result implies that a compact binary pr…
Data selection and the determination of systematic uncertainties in the spectroscopic measurements of neutron star radii from thermonuclear X-ray bursts have been the subject of numerous recent studies. In one approach, the uncertainties and outliers were determined by a data-driven Bayesian mixture model, whereas in a second approach, data selection was performed by requiring that the observations follow theoretical expectations. We show here that, due to inherent limitations in the data, the theoretically expected trends are not discernible in the majority of X-ray bursts even if they are pr…
The observational era of gravitational-wave astronomy began in the Fall of 2015 with the detection of GW150914. One potential type of detectable gravitational wave is short-duration gravitational-wave bursts, whose waveforms can be difficult to predict. We present the framework for a new detection algorithm for such burst events -- \textit{oLIB} -- that can be used in low-latency to identify gravitational-wave transients independently of other search algorithms. This algorithm consists of 1) an excess-power event generator based on the Q-transform -- \textit{Omicron} --, 2) coincidence of thes…
A tiny fraction of observed gamma-ray bursts (GRBs) may be lensed. The time delays induced by the gravitational lensing are milliseconds to seconds if the point lenses are intermediate-mass black holes. The prompt emission of the lensed GRBs, in principle, should have repeated pulses with identical light curves and spectra but different fluxes and slightly offset positions. In this work, we search for such candidates within the GRBs detected by Fermi/GBM, Swift/BAT, and HXMT/HE and report the identification of an attractive event GRB 200716C that consists of two pulses. Both the autocorrelatio…
Gamma-ray burst (GRB) prompt emission is highly beamed, and understanding the jet geometry and beaming configuration can provide information on the poorly understood central engine and circum-burst environment. Prior to the advent of gravitational-wave astronomy, astronomers relied on observations of jet breaks in the multi-wavelength afterglow to determine the GRB opening angle, since the observer's viewing angle relative to the system cannot be determined from the electromagnetic data alone. Gravitational-wave observations, however, provide an independent measurement of the viewing angle. We…
The standard noise model in gravitational wave (GW) data analysis assumes detector noise is stationary and Gaussian distributed, with a known power spectral density (PSD) that is usually estimated using clean off-source data. Real GW data often depart from these assumptions, and misspecified parametric models of the PSD could result in misleading inferences. We propose a Bayesian semiparametric approach to improve this. We use a nonparametric Bernstein polynomial prior on the PSD, with weights attained via a Dirichlet process distribution, and update this using the Whittle likelihood. Posterio…
Gamma-ray bursts (GRBs) detected at high redshift can be used to trace the Hubble diagram of the Universe. However, the distance calibration of GRBs is not as easily as that of type Ia supernovae (SNe Ia). For the calibrating method based on the empirical luminosity correlations, there is an underlying assumption that the correlations should be universal over the whole redshift range. In this paper, we investigate the possible redshift dependence of six luminosity correlations with a completely model-independent deep learning method. We construct a network combining the Recurrent Neural Networ…
