PaperlayerView exact revision on arXiv

Source-linked AI summary

X-Pipeline: An analysis package for autonomous gravitational-wave burst searches

Patrick J. Sutton, Gareth Jones, Shourov Chatterji, Peter Michael Kalmus, Isabel Leonor, Stephen Poprocki, Jameson Rollins, Antony Searle, Leo Stein, Massimo Tinto, Michal Was

arXiv:0908.3665v2gr-qc

TL;DR

Slow, laborious burst-search analysis motivates autonomous methods that can identify candidates for follow-up. X-Pipeline automates coherent triggered searches, including tuning and background estimation using independent data samples. On GRB 031108, its predicted sensitivity was approximately a factor of 1.7 better than the cross-correlation pipeline.

  • Problem

    Burst searches face non-stationary detector noise, unknown waveforms, and laborious optimization, complicating rapid, robust identification of weak signals.

    Source: §I · p. 1

  • Method

    X-Pipeline performs coherent triggered burst searches and automates tuning and sensitivity estimation using separate data samples for tuning and evaluation.

    Source: §I · p. 2, §3 · p. 13

  • Results

    The predicted X-Pipeline sensitivity was approximately a factor of 1.7 better than that of the cross-correlation pipeline.

    Source: A. Analysis · p. 15

  • Takeaways & Limitations

    The planned S6-VSR2 autonomous search aimed to complete each GRB analysis within 24 hours of its trigger.

    Source: §V · p. 16

Abstract

from arXiv · show

Autonomous gravitational-wave searches -- fully automated analyses of data that run without human intervention or assistance -- are desirable for a number of reasons. They are necessary for the rapid identification of gravitational-wave burst candidates, which in turn will allow for follow-up observations by other observatories and the maximum exploitation of their scientific potential. A fully automated analysis would also circumvent the traditional "by hand" setup and tuning of burst searches that is both labourious and time consuming. We demonstrate a fully automated search with X-Pipeline, a software package for the coherent analysis of data from networks of interferometers for detecting bursts associated with GRBs and other astrophysical triggers. We discuss the methods X-Pipeline uses for automated running, including background estimation, efficiency studies, unbiased optimal tuning of search thresholds, and prediction of upper limits. These are all done automatically via Monte Carlo with multiple independent data samples, and without requiring human intervention. As a demonstration of the power of this approach, we apply X-Pipeline to LIGO data to search for gravitational-wave emission associated with GRB 031108. We find that X-Pipeline is sensitive to signals approximately a factor of 2 weaker in amplitude than those detectable by the cross-correlation technique used in LIGO searches to date. We conclude with the prospects for running X-Pipeline as a fully autonomous, near real-time triggered burst search in the next LSC-Virgo Science Run.

I. INTRODUCTION

Rapid, autonomous burst searches are motivated by the need to identify candidates promptly for follow-up and by the laborious, slow nature of conventional analysis. X-Pipeline uses coherent network analysis, with noise-weighted detector data and sky-dependent responses, as the basis for triggered searches.

I. INTRODUCTION

  • Rapid, confident gravitational-wave burst candidates are vital for follow-up by other observatories, while conventional analyses can take years and detector characterization and optimization are laborious.Autonomous, self-tuning packages are proposed to process data rapidly and adapt search parameters to network and background changes.Source: §I · pp. 1–2

II. COHERENT ANALYSIS FOR GRAVITATIONAL-WAVE BURST DETECTION

  • Coherent methods combine multiple detectors before processing, can reject glitches, and are relatively easy to tune, making them useful for rapid searches.For triggered searches, known sky positions and relatively small data volumes can make the computational cost modest.Source: §II · p. 2

A. Formulation

  • Detector outputs combine gravitational-wave polarizations, antenna responses, time delays, and noise; noise-spectrum weighting places network sensitivity information in the response matrix.Coherent combinations generally must be recomputed for each frequency bin and sky position.Source: A. Formulation · pp. 3–4

B. Standard Likelihood

The standard likelihood provides a coherent detection statistic when the waveform is not known in advance. It assumes Gaussian noise and maximizes the likelihood ratio over waveform values in each time-frequency pixel.

B. Standard Likelihood

  • Assuming Gaussian noise, the likelihood ratio compares the probability of measured whitened data with a known waveform to the probability under the no-signal hypothesis.For multiple time-frequency pixels, the likelihood is formed from the data across those pixels.Source: B. Standard Likelihood · p. 4
  • Because the waveform is not known a priori, its values in each time-frequency pixel are treated as free parameters and fitted to maximize the likelihood ratio.The likelihood ratio is quadratic in the waveform, so maximizing it yields a linear equation for the best-fit waveform.Source: B. Standard Likelihood · p. 4
  • Substituting the best-fit waveform into the likelihood ratio gives the standard likelihood used as a detection statistic.The factor of 2 in the defined statistic is a matter of convention.Source: B. Standard Likelihood · p. 4

C. Projection Operators and the Null Energy

The standard likelihood keeps the data energy consistent with a gravitational wave from a given sky position, while the orthogonal null projection measures energy inconsistent with that hypothesis.

C. Projection Operators and the Null Energy

  • The standard likelihood is the maximum data energy consistent with a gravitational wave from a given sky position.It projects data into the subspace spanned by F+ and F×.Source: C. Projection Operators and the Null… · p. 4
  • The total energy is an incoherent statistic containing autocorrelation terms but no cross-correlation terms.For a single detector, it is the quantity computed per time-frequency pixel in an excess-power search.Source: C. Projection Operators and the Null… · p. 4
  • The null projection cancels the gravitational-wave signal, leaving null energy that measures the minimum data energy inconsistent with the given-sky-position hypothesis.The null projection operator is P_null = I − P_GW.Source: C. Projection Operators and the Null… · p. 4
  • With a known sky position, projection removes some noise without removing signal; searching unknown positions applies many projections and incurs a false-alarm penalty.Small calibration, sky-position, or power-spectrum errors affect signal energy only at second order.Source: C. Projection Operators and the Null… · p. 4

D. Dominant Polarization Frame and Other Likelihoods

The dominant polarization frame (DPF) provides a network-tailored basis for coherent burst statistics, with orthogonal polarization responses ordered by antenna response. X-Pipeline also supports other likelihoods, though they are not considered here.

D. Dominant Polarization Frame and Other Likelihoods

  • The DPF aligns F+ and F× with orthogonal basis directions ordered by maximum and minimum network antenna response.Unlike source-referenced bases used for modeled signals, the DPF is tailored to the detector network at each frequency.Source: D. Dominant Polarization Frame and… · p. 5
  • The DPF polarization rotation depends on sky position and frequency because the antenna responses are noise-weighted.The frame is constructed by rotating the antenna response vectors until they are orthogonal and |F+(ψ)| exceeds |F×(ψ)|.Source: D. Dominant Polarization Frame and… · p. 5
  • In the DPF, the normalized antenna responses e+ and e× form part of an orthonormal coordinate system for detector data.Rotating to this frame is mathematically equivalent to a singular value decomposition of F.Source: D. Dominant Polarization Frame and… · p. 5
  • The DPF does not specify a null-space basis, and choosing a convenient one for null-energy use is outside this discussion.Source: D. Dominant Polarization Frame and… · p. 5
  • The plus, cross, standard, and soft-constraint likelihoods use different combinations or constraints on the two DPF polarization directions.The plus-energy or hard-constraint likelihood is the energy in h+; the cross energy is defined analogously.Source: D. Dominant Polarization Frame and… · pp. 5–6
  • X-Pipeline includes other likelihood-based statistics, but this discussion does not consider them.Examples include Tikhonov regularization, sky-map variability, modified constraint likelihoods, and Bayesian formulations.Source: D. Dominant Polarization Frame and… · p. 6

E. Statistical Properties

For a time-frequency region and sky position chosen in advance, the coherent energy measures have simple chi-squared distributions in Gaussian noise. Their projection dimensions determine degrees of freedom and contribute to the expected noise fluctuations.

E. Statistical Properties

  • For a priori chosen pixels and sky position, each listed energy follows a χ2 distribution with 2NpDproj degrees of freedom.Np is the number of pixels, and Dproj is the number of projection dimensions.Source: E. Statistical Properties · p. 6
  • Dproj is 1 for E+ and E×, 2 for ESL, and D for Etot; it is D−2 for Enull except for the H1-H2 null stream, where it is D−1.The H1-H2 sub-network is sensitive to one gravitational-wave polarization, so only one dimension is removed in forming its null stream.Source: E. Statistical Properties · p. 6
  • The factor of 2 in the degrees of freedom arises because the data are complex.The non-centrality parameter λ is the expected squared matched-filter signal-to-noise ratio in the selected time-frequency region after projection.Source: E. Statistical Properties · p. 6
  • The table reports expected means and standard deviations for the energy measures when the correct sky position and time-frequency region are known a priori.Its standard-deviation values assume a non-aligned detector network; Esoft values are approximate because ε varies with frequency.Source: E. Statistical Properties · p. 6
  • Projecting onto fewer dimensions is expected to reduce noise, while coherent consistency tests can allow ESL to retain signal-to-noise from both polarizations.E+ uses one direction, ESL and Esoft use two, and Etot uses all data dimensions.Source: E. Statistical Properties · p. 7

F. Incoherent Energies and Background Rejection

Coherent consistency tests distinguish detector-correlated gravitational-wave signals from noise glitches by comparing coherent and incoherent energies. The null-energy veto exploits the expected signal cancellation in the null stream and uses an event-energy-dependent threshold in X-Pipeline.

F. Incoherent Energies and Background Rejection

  • For glitches, coherent likelihoods can be large, so background rejection compares each coherent energy with its incoherent counterpart.The energies are motivated by stationary Gaussian noise, whereas real detector noise includes short excess-strain glitches that can mimic bursts.Source: F. Incoherent Energies and Background… · p. 7
  • The null projection contains noise but cancels gravitational-wave signal, whereas glitches generally contribute to the null space because they lack the detector relationships set by F+ and F×.The coherent veto therefore keeps transients whose null energy is small relative to incoherent null energy.Source: F. Incoherent Energies and Background… · p. 7
  • For glitches, null energy is expected to be dominated by autocorrelation components, while for strong gravitational waves the correlated detector signal cancels in the null stream but remains in incoherent null energy.The incoherent energy is the autocorrelation part of null energy.Source: F. Incoherent Energies and Background… · p. 7
  • X-Pipeline varies the null-veto threshold with event energy because statistical fluctuations can make null energy small relative to incoherent null energy for weaker glitches.The cited coherent veto is particularly effective at eliminating large-amplitude glitches.Source: F. Incoherent Energies and Background… · p. 7
  • A gravitational-wave signal should build coherently across detectors, while a glitch is expected to have similar coherent and incoherent energies.For the standard likelihood, the stated signal expectation is ESL > ISL.Source: F. Incoherent Energies and Background… · p. 7
  • At least one polarization energy can show coherent buildup for a gravitational wave, enabling coherent glitch tests even without a null stream.For a signal predominantly in h+ or h× in the DPF, the corresponding polarization energy is expected to exceed its incoherent counterpart.Source: F. Incoherent Energies and Background… · pp. 7–8
  • The listed incoherent energies sum to the total energy, as do the corresponding coherent energies.The cross-correlation contributions to the coherent-minus-incoherent differences cancel across the polarization and null energies.Source: F. Incoherent Energies and Background… · p. 8

III. OVERVIEW OF X-PIPELINE

X-Pipeline is a MATLAB-based package for coherent searches for gravitational-wave bursts in arbitrary detector networks. Users specify the detectors, data intervals, coherent energies, sky positions, and analysis parameters; the pipeline produces candidate signals for each sky position.

III. OVERVIEW OF X-PIPELINE

  • X-Pipeline performs coherent searches for gravitational-wave bursts in data from arbitrary detector networks.The overview describes the main steps of a triggered burst search and how candidate signals are identified.Source: §III · p. 8

A. Preliminaries

  • Users specify the detector set, data intervals, coherent energies, sky positions, and analysis parameters such as FFT lengths.Source: A. Preliminaries · p. 8
  • For each specified sky position, X-Pipeline constructs time-frequency maps of reconstructed h+, h×, and null streams, then identifies clusters with large coherent-energy values.Source: A. Preliminaries · p. 8

B. Time-frequency maps

X-Pipeline identifies candidate bursts by clustering high-energy pixels in time-frequency maps, comparing clusters across analysis times, and applying coherent glitch vetoes. Its median-tracking veto follows the measured background distribution; separate data-quality vetoes are defined outside the package.

C. Clustering and Event Identification

  • Clusters of neighboring high-statistic pixels become candidate events, with the pixel statistics summed and an approximate χ2-based significance assigned.The method assumes connected time-frequency signal shapes, an assumption stated to hold for many modeled signals such as low-mass inspirals and ringdowns.Source: C. Clustering and Event Identification · p. 9
  • Using several analysis times addresses unknown signal duration; overlapping clusters are compared and only the most significant is retained.Pixel aspect ratio trades time resolution against frequency resolution, and the preferred pixel size minimizes the number of pixels spanned by the signal.Source: C. Clustering and Event Identification · p. 9

D. Glitch rejection

  • Coherent glitch vetoes compare coherent and incoherent energies because noise glitches tend to correlate them; ratio tests use user-set or automatically selected thresholds.The two-sided ratio tests accept clusters sufficiently far above or below the diagonal.Source: D. Glitch rejection · pp. 9–10
  • The median-tracking veto fits a quadratic to binned background medians and smoothly joins it to I = E at high E.The curve is described as ad hoc but as providing a good fit to the observed glitch distribution.Source: D. Glitch rejection · p. 10
  • The median-tracking veto separates simulated signals from background clusters in (Enull, Inull) space, including signals weaker than strong background glitches.Clusters below the dashed threshold are discarded; the figure colors points by log10 S.Source: D. Glitch rejection · p. 10, Figure 4 · p. 10
  • Data-quality vetoes can also reject clusters overlapping periods flagged for non-gravitational disturbances, but those vetoes are defined independently of X-Pipeline.Source: D. Glitch rejection · p. 10

E. Triggered search: tuning and upper limits

For triggered searches, X-Pipeline uses the known GRB sky position to perform coherent analysis and evaluates the loudest on-source event against an empirical background. Off-source data and time slides provide background samples, with special handling for the co-located Hanford detectors.

E. Triggered search: tuning and upper limits

1. Detection Procedure

  • The loudest veto-surviving on-source cluster is compared with an off-source distribution to assess whether it is statistically significant.A threshold can be set so background noise has a specified small probability, such as 1%, of producing a louder on-source cluster.Source: §1 · p. 11
  • Off-source segments are analyzed like the on-source data to estimate background; time shifts can provide up to approximately 1000 times the on-source data and support sub-1% probability estimates.The usual off-source interval is within ±1.5 hours of the GRB, excluding the on-source interval.Source: §1 · p. 11
  • For H1-H2 networks, time shifts do not account for simultaneous local environmental glitches, so H1 is not shifted relative to H2 unless they are the only detectors operating.In that case, the local probability is computed both with and without time slides for a consistency check.Source: §1 · p. 11

2. Upper Limits

X-Pipeline sets upper limits by injecting simulated signals into on-source data and measuring whether they produce events louder than the observed on-source maximum. The resulting 90% limit is expressed in hrss, whose interpretation depends on waveform family, frequency, and sky position.

2. Upper Limits

  • The 90% confidence-level upper limit is the minimum signal amplitude for which at least 90% of signals would produce a cluster louder than the on-source maximum.The procedure repeats injections at different hrss amplitudes and measures the loudest surviving cluster associated with each injection.Source: §2 · pp. 11–12
  • hrss upper limits depend on waveform family, frequency, and source sky position because hrss does not include detector sensitivity.For narrow-band signals, hrss can also be linked to emitted gravitational-wave energy assuming isotropic radiation.Source: §2 · p. 12
  • The injection study selects waveform families, randomizes their parameters, adds signals to on-source data, and measures the percentage exceeding the observed loudest-event significance.The procedure is repeated over hrss amplitudes for each waveform family.Source: §2 · p. 12

3. Tuning and Closed-Box Analyses

X-Pipeline tunes coherent glitch-veto thresholds using a closed-box analysis, keeping the on-source data blind to avoid biasing the upper limit. Independent data samples separate threshold tuning from sensitivity estimation.

3. Tuning and Closed-Box Analyses

  • The closed-box analysis selects veto thresholds that minimize an upper limit estimated from off-source data and simulated injections, without using the on-source data.Testing a range of thresholds optimizes the trade-off between rejecting glitches and accepting signals.Source: §3 · p. 12
  • Off-source segments and injection clusters are randomly split into separate tuning and upper-limit estimation samples to prevent tuning and sensitivity estimation from using the same data.For each trial threshold combination, the tuning sample supplies the loudest surviving background events and a dummy on-source segment near the 95th percentile.Source: §3 · pp. 12–13
  • The selected thresholds give the lowest dummy-on-source upper limit, with upper limits averaged across waveform families when multiple families are tested.The second sample is then analyzed with the fixed thresholds, using the 50th percentile of the loudest-event distribution to choose its dummy on-source segment.Source: §3 · p. 13
  • The 95th percentile targets loud background glitches during tuning, while the 50th percentile represents a typical on-source loudest event under the null hypothesis for sensitivity estimation.Using different samples for tuning and sensitivity estimation avoids bias from choosing cuts on the same data used to estimate sensitivity.Source: §3 · p. 13
  • X-Pipeline automatically reports optimized thresholds and predicted upper limits, and the planned S6/VSR2 workflow would automatically open the on-source box after closed-box tuning.For S5/VSR1, users still reran post-processing on the on-source data with fixed optimized thresholds.Source: §3 · p. 13

4. Statistical and Systematic Errors

X-Pipeline’s GRB 031108 closed-box analysis estimated 90%-confidence upper limits about 1.7 times better than the cross-correlation pipeline. The analysis also accounts for calibration and sky-position uncertainties by perturbing simulated signals.

4. Statistical and Systematic Errors

  • The principal stated uncertainties are detector calibration in amplitude, phase, and relative timing, and uncertainty in the GRB sky position.The injection engine perturbs these quantities according to Gaussian distributions matched to detector calibration uncertainties and the reported GRB error-box width, effectively marginalizing the tuning and upper limits over them.Source: §4 · p. 13
  • For the S5-VSR1 GRB search, perturbed injections were unavailable during the original analysis, so error impacts were re-estimated on a small subset of the sample.For S6-VSR2, calibration and sky-position uncertainties were included in simulations for all GRBs from the beginning.Source: §4 · p. 13

A. Analysis

  • The null-stream test separated simulated signals from loud background clusters because the injections lay above the diagonal in (Inull, Enull), allowing the tuned veto to reject most loud off-source clusters while accepting most injections.The analysis found that H2’s lower sensitivity gives it little weight in E+, while the null-stream weighting reverses the detector weights.Source: A. Analysis · p. 14, Figure 6 · p. 14, Figure 7 · p. 15

IV. GRB 031108; A. Analysis

  • A factor of 1.7 better predicted sensitivity than the cross-correlation pipeline corresponded to a factor of 1.73, approximately 5, increase in search volume for GRB 031108.The comparison used the same simulated waveforms as the cross-correlation search; Table III reports the estimated X-Pipeline and actual cross-correlation upper limits.Source: §IV · pp. 13–14, A. Analysis · p. 15, Table III · p. 16

A. Analysis

  • In the H1-H2 analysis, the coherent glitch test limited sensitivity at amplitudes tracking H2’s noise spectrum and corresponding to a matched-filter signal-to-noise ratio of approximately 5 in H2.The test requires measurable correlation between detectors, which requires a minimum signal-to-noise ratio in each; the aggressive 95th-percentile tuning suppresses loud background events.Source: A. Analysis · pp. 14–16, Figure 5 · p. 14
  • The factor-of-1.7 sensitivity improvement was attributed partly to an approximately 1.3 gain from ESL and an approximately 1.2 gain from clustering, while the rough estimates omit non-Gaussian background effects and veto-limited sensitivity.ESL adds autocorrelation terms, and X-Pipeline clusters typically used 10–30 pixels versus approximately 50 for the cross-correlation statistic.Source: A. Analysis · p. 16

V. AUTONOMOUS RUNNING

X-Pipeline’s S6/VSR2 goal was a fully autonomous GRB analysis within 24 hours of a trigger. Automated GCN-triggered jobs were operational, with open-box results available as soon as six hours after an alert.

V. AUTONOMOUS RUNNING

  • For S6/VSR2, the goal was to complete each GRB analysis within 24 hours of its trigger, extending X-Pipeline beyond the offline S5-VSR1 search.S5-VSR1 processing had finished almost two years after the last GRB in that sample was observed.Source: §V · p. 16

A. Automated launch of X-Pipeline by GCN triggers

  • GCN scripts parse trigger information, check for data availability, launch and monitor event-generation and post-processing jobs, then publish results and email analysts.The triggering scripts were operational and autonomously analyzing Swift GRBs, with open-box results available as soon as six hours after a GCN alert.Source: A. Automated launch of X-Pipeline by… · pp. 16–17
  • For S6/VSR2, launch scripts were being adapted to cover Fermi’s larger sky-position error regions, while the simulated waveform suite was expanded to include binary inspirals.Typical Fermi position uncertainty was several degrees, compared with a few arcminutes for Swift; the added inspirals were binary neutron-star and black-hole–neutron-star systems.Source: A. Automated launch of X-Pipeline by… · p. 17
Loading 0908.3665v2…