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Register a new userStealth Bias in Gravitational-Wave Parameter Estimation
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Inspiraling binaries of compact objects are primary targets for current and future gravitational-wave observatories. Waveforms computed in General Relativity are used to search for these sources, and will probably be used to extract source parameters from detected signals. However, if a different theory of gravity happens to be correct in the strong-field regime, source-parameter estimation may be affected by a fundamental bias: that is, by systematic errors induced due to the use of waveforms derived in the incorrect theory. If the deviations from General Relativity are not large enough to be detectable on their own and yet these systematic errors remain significant (i.e., larger than the statistical uncertainties in parameter estimation), fundamental bias cannot be corrected in a single observation, and becomes stealth bias. In this article we develop a scheme to determine in which cases stealth bias could be present in gravitational-wave astronomy. For a given observation, the answer depends on the detection signal-to-noise ratio and on the strength of the modified-gravity correction. As an example, we study three representative stellar-mass binary systems that will be detectable with second-generation ground-based observatories. We find that significant systematic bias can occur whether or not modified gravity can be positively detected, for correction strengths that are not currently excluded by any other experiment. Thus, stealth bias may be a generic feature of gravitational-wave detections, and it should be considered and characterized, using expanded models such as the parametrized post-Einstein framework, when interpreting the results of parameter-estimation analyses.
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One of the main bottlenecks in gravitational wave (GW) astronomy is the high cost of performing parameter estimation and GW searches on the fly. We propose a novel technique based on Reduced Order Quadratures (ROQs), an application and data-specific quadrature rule, to perform fast and accurate likelihood evaluations. These are the dominant cost in Markov chain Monte Carlo (MCMC) algorithms, which are widely employed in parameter estimation studies, and so ROQs offer a new way to accelerate GW parameter estimation. We illustrate our approach using a four dimensional GW burst model embedded in noise. We build an ROQ for this model, and perform four dimensional MCMC searches with both the standard and ROQs quadrature rules, showing that, for this model, the ROQ approach is around 25 times faster than the standard approach with essentially no loss of accuracy. The speed-up from using ROQs is expected to increase for more complex GW signal models and therefore has significant potential to accelerate parameter estimation of GW sources such as compact binary coalescences.
Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution constructed using Gaussian process regression (GPR). As an example, we apply this technique to the measurement of chirp mass using (simulated) gravitational-wave signals from binary black holes that could be observed using advanced-era gravitational-wave detectors. Unless properly accounted for, uncertainty in the gravitational-wave templates could be the dominant source of error in studies of these systems. We explain our approach in detail and provide proofs of various features of the method, including the limiting behavior for high signal-to-noise, where systematic model uncertainties dominate over noise errors. We find that the marginalized likelihood constructed via GPR offers a significant improvement in parameter estimation over the standard, uncorrected likelihood both in our simple one-dimensional study, and theoretically in general. We also examine the dependence of the method on the size of training set used in the GPR; on the form of covariance function adopted for the GPR, and on changes to the detector noise power spectral density.
Since the very first detection of gravitational waves from the coalescence of two black holes in 2015, Bayesian statistical methods have been routinely applied by LIGO and Virgo to extract the signal out of noisy interferometric measurements, obtain point estimates of the physical parameters responsible for producing the signal, and rigorously quantify their uncertainties. Different computational techniques have been devised depending on the source of the gravitational radiation and the gravitational waveform model used. Prominent sources of gravitational waves are binary black hole or neutron star mergers, the only objects that have been observed by detectors to date. But also gravitational waves from core collapse supernovae, rapidly rotating neutron stars, and the stochastic gravitational wave background are in the sensitivity band of the ground-based interferometers and expected to be observable in future observation runs. As nonlinearities of the complex waveforms and the high-dimensional parameter spaces preclude analytic evaluation of the posterior distribution, posterior inference for all these sources relies on computer-intensive simulation techniques such as Markov chain Monte Carlo methods. A review of state-of-the-art Bayesian statistical parameter estimation methods will be given for researchers in this cross-disciplinary area of gravitational wave data analysis.
Reliable low-latency gravitational wave parameter estimation is essential to target limited electromagnetic followup facilities toward astrophysically interesting and electromagnetically relevant sources of gravitational waves. In this study, we examine the tradeoff between speed and accuracy. Specifically, we estimate the astrophysical relevance of systematic errors in the posterior parameter distributions derived using a fast-but-approximate waveform model, SpinTaylorF2 (STF2), in parameter estimation with lalinference_mcmc. Though efficient, the STF2 approximation to compact binary inspiral employs approximate kinematics (e.g., a single spin) and an approximate waveform (e.g., frequency domain versus time domain). More broadly, using a large astrophysically-motivated population of generic compact binary merger signals, we report on the effectualness and limitations of this single-spin approximation as a method to infer parameters of generic compact binary sources. For most low-mass compact binary sources, we find that the STF2 approximation estimates compact binary parameters with biases comparable to systematic uncertainties in the waveform. We illustrate by example the effect these systematic errors have on posterior probabilities most relevant to low-latency electromagnetic followup: whether the secondary is has a mass consistent with a neutron star; whether the masses, spins, and orbit are consistent with that neutron stars tidal disruption; and whether the binarys angular momentum axis is oriented along the line of sight.
The first detection of a gravitational-wave signal of a coalescence of two black holes marked the beginning of the era of gravitational-wave astronomy, which opens exciting new possibilities in the fields of astronomy, astrophysics and cosmology. The currently operating detectors of the LIGO and Virgo collaborations are sensitive at relatively high frequencies, from 10 Hz up to about a kHz, and are able to detect gravitational waves emitted in a short time frame of less than a second (binary black holes) to minutes (binary neutron stars). Future missions like LISA will be sensitive in lower frequency ranges, which will make it possible to detect gravitational waves emitted long before these binaries merge. In this article, we investigate the possibilities for parameter estimation using the Fisher-matrix formalism with combined information from present and future detectors in different frequency bands. The detectors we consider are the LIGO/Virgo detectors, the Einstein Telescope (ET), the Laser Interferometer Space Antenna (LISA), and the first stage of the Deci- Hertz Interferometer Gravitational wave Observatory (B-DECIGO). The underlying models are constructed in time domain, which allows us to accurately model long-duration signal observations with multiband (or broadband) detector networks on parameter estimation. We assess the benefit of combining information from ground-based and space-borne detectors, and how choices of the orbit of B-DECIGO influence parameter estimates.
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