Information-theoretic approach to the gravitational-wave burst detection problem

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 detection algorithm for such burst events—oLIB—that can be used in low latency to identify gravitational-wave transients. This algorithm consists of (1) an excess-power event generator based on the Q transform—Omicron—, (2) coincidence of these events across a detector network, and (3) an analysis of the coincident events using a Markov chain Monte Carlo Bayesian evidence calculator—LALInferenceBurst. These steps compress the full data streams into a set of Bayes factors for each event. Through this process, we use elements from information theory to minimize the amount of information regarding the signal-versus-noise hypothesis that is lost. We optimally extract this information using a likelihood-ratio test to estimate a detection significance for each event. Using representative archival LIGO data across different burst waveform morphologies, we show that the algorithm can detect gravitational-wave burst events of astrophysical strength in realistic instrumental noise. We also demonstrate that the combination of Bayes factors by means of a likelihood-ratio test can improve the detection efficiency of a gravitational-wave burst search. Finally, we show that oLIB’s performance is robust against the choice of gravitational-wave populations used to model the likelihood-ratio test likelihoods.

Figure 1

Schematic of how information is compressed into a significance estimate within the oLIB algorithm. Ideally, sufficient statistics allow for lossless data compression, and the LRT allows for optimal information extraction.

Figure 2

A flow chart illustrating the hierarchical structure of the oLIB algorithm. Calibrated strain data and analyzable time segments are fed into Omicron, which produces single-interferometer (IFO) events. The events are down-selected via incoherent clustering, data-quality vetoes, and coincidence. Sets of the most significant analysis (0-lag) and background (time slide) events are passed onto LIB. The Bayes factors produced by LIB (BSN and BCI) are combined using a LRT. The LRT also requires likelihood models for both the detection (signal) and nondetection (noise) hypotheses. Finally, the LRT provides a measure of each 0-lag event’s detection significance.

Figure 3

The rates at which the events generated by Omicron exceeded a given value of SNR in Hanford (top) and Livingston (bottom). These events are grouped by the down-selection steps they have just survived: either clustering, data-quality vetoes, timing coincidence, or LIB-window clustering (LC). The 68% confidence regions shown are derived from a binomial process with a uniform prior on the true rate.

Figure 4

The one-dimensional likelihoods for each Bayes factor. In this figure, the signal training population consisted of both sine-Gaussian and white-noise burst signals. The likelihood ratio $\mathrm{\Lambda }$ is found by taking the ratio of the signal and noise likelihoods.

Figure 5

The two-dimensional likelihoods for the Bayes factors. The contours shown correspond to the 0.5-sigma, 1-sigma, 1.5-sigma, and 2-sigma central confidence regions. The likelihood ratio $\mathrm{\Lambda }$ is found by taking the ratio of the signal and noise likelihoods.

Figure 6

The FAR achieved by setting a given likelihood-ratio threshold for detection. The LRT shown here is trained on both sine-Gaussian and white-noise burst signal populations and is evaluated using BCI and BSN as search statistics. The 68% confidence regions shown are derived from a binomial process with a uniform prior on the true rate.

Figure 7

The detection efficiency as a function of the optimal network SNR at a FAR of 1 per decade for three different morphologies of injected waveforms: sine-Gaussian waveforms (top) with $f_0=153\mathrm{Hz}$ and $Q=8.9$, Gaussian waveforms (middle) with $\tau =2.5\mathrm{ms}$, and white-noise burst waveforms (bottom) with $f_0=1000\mathrm{Hz}$, $\mathrm{\Delta }=10\mathrm{Hz}$, and $\tau =100\mathrm{ms}$. The LRT used here is trained on both sine Gaussians and white-noise bursts and is evaluated using both the BCI and the BSN as search statistics. The 68% confidence region shown is derived from a binomial process with a uniform prior on the true detection efficiency.