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1. Computational techniques for parameter estimation of gravitational wave signals

   https://doi.org/10.1002/wics.1532  

   Meyer, Renate ; Edwards, Matthew_C ; Maturana‐Russel, Patricio ; Christensen, Nelson ( September 2020 , WIREs Computational Statistics)

   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.

   This article is categorized under:

   Applications of Computational Statistics > Signal and Image Processing and Coding

   Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)

   Statistical Models > Time Series Models

    

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2. Population synthesis and parameter estimation of neutron stars with continuous gravitational waves and third-generation detectors

   https://doi.org/10.1093/mnras/stad3811  

   Hua, Yuhan ; Wette, Karl ; Scott, Susan M. ; Pitkin, Matthew D. ( December 2023 , Monthly Notices of the Royal Astronomical Society)

   Precise measurement of stellar properties through the observation of continuous gravitational waves from spinning non-axisymmetric neutron stars can shed light onto new physics beyond terrestrial laboratories. Although hitherto undetected, prospects for detecting continuous gravitational waves improve with longer observation periods and more sensitive gravitational wave detectors. We study the capability of the Advanced Laser Interferometer Gravitational-Wave Observatory, and the Einstein Telescope to measure the physical properties of neutron stars through continuous gravitational wave observations. We simulate a population of Galactic neutron stars, assume continuous gravitational waves from the stars have been detected, and perform parameter estimation of the detected signals. Using the estimated parameters, we infer the stars’ moments of inertia, ellipticities, and the components of the magnetic dipole moment perpendicular to the rotation axis. The estimation of the braking index proved challenging and is responsible for the majority of the uncertainties in the inferred parameters. Using the Einstein Telescope with an observation period of $5\, {\rm {yr}}$, point estimates using median can be made on the moments of inertia with error of $\sim 10\!-\!100~{{\ \rm per\ cent}}$ and on the ellipticities with error of $\sim 5\!-\!50~{{\ \rm per\ cent}}$, subject to the inference of the braking index. The perpendicular magnetic dipole moment could not be accurately inferred for neutron stars that emit mainly gravitational waves.

    

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3. Statistically-informed deep learning for gravitational wave parameter estimation

   https://doi.org/10.1088/2632-2153/ac3843  

   Shen, Hongyu ; Huerta, E A ; O’Shea, Eamonn ; Kumar, Prayush ; Zhao, Zhizhen ( November 2021 , Machine Learning: Science and Technology)

   Abstract We introduce deep learning models to estimate the masses of the binary components of black hole mergers, ( m 1 , m 2 ) , and three astrophysical properties of the post-merger compact remnant, namely, the final spin, a f , and the frequency and damping time of the ringdown oscillations of the fundamental ℓ = m = 2 bar mode, ( ω R , ω I ) . Our neural networks combine a modified WaveNet architecture with contrastive learning and normalizing flow. We validate these models against a Gaussian conjugate prior family whose posterior distribution is described by a closed analytical expression. Upon confirming that our models produce statistically consistent results, we used them to estimate the astrophysical parameters ( m 1 , m 2 , a f , ω R , ω I ) of five binary black holes: GW150914 , GW170104 , GW170814 , GW190521 and GW190630 . We use PyCBC Inference to directly compare traditional Bayesian methodologies for parameter estimation with our deep learning based posterior distributions. Our results show that our neural network models predict posterior distributions that encode physical correlations, and that our data-driven median results and 90% confidence intervals are similar to those produced with gravitational wave Bayesian analyses. This methodology requires a single V100 NVIDIA GPU to produce median values and posterior distributions within two milliseconds for each event. This neural network, and a tutorial for its use, are available at the Data and Learning Hub for Science . 

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4. Rapid localization of gravitational wave hosts with FIGARO

   https://doi.org/10.1093/mnrasl/slac101  

   Rinaldi, Stefano ; Del Pozzo, Walter ( September 2022 , Monthly Notices of the Royal Astronomical Society: Letters)

   The copious scientific literature produced after the detection of GW170817 electromagnetic counterpart demonstrated the importance of a prompt and accurate localization of the gravitational wave within the comoving volume. In this letter, we present figaro, a ready to use and publicly available software that relies on Bayesian non-parametrics. figaro is designed to run in parallel with parameter estimation algorithms to provide updated three-dimensional volume localization information. Differently from any existing algorithms, the analytical nature of the figaro reconstruction allows a ranking of the entries of galaxy catalogues by their probability of being the host of a gravitational wave event, hence providing an additional tool for a prompt electromagnetic follow up of gravitational waves. We illustrate the features of figaro on binary black holes as well as on GW170817. Finally, we demonstrate the robustness of figaro by producing so-called pp-plots and we present a method based on information entropy to assess when, during the parameter estimation run, it is reasonable to begin releasing skymaps.

    

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5. Measuring the eccentricity of GW170817 and GW190425

   https://doi.org/10.1093/mnras/staa2120  

   Lenon, Amber K ; Nitz, Alexander H ; Brown, Duncan A ( September 2020 , Monthly Notices of the Royal Astronomical Society)

   null (Ed.)

   ABSTRACT Two binary neutron star mergers, GW170817 and GW190425, have been detected by Advanced LIGO and Virgo. These signals were detected by matched-filter searches that assume that the star’s orbit has circularized by the time their gravitational-wave emission is observable. This suggests that their eccentricity is low, but full parameter estimation of their eccentricity has not yet been performed. We use gravitational-wave observations to measure the eccentricity of GW170817 and GW190425. We find that the eccentricity at a gravitational-wave frequency of 10 Hz is e ≤ 0.024 and e ≤ 0.048 for GW170817 and GW190425, respectively (90 per cent confidence). This is consistent with the binaries being formed in the field, as such systems are expected to have circularized to e ≤ 10−4 by the time they reach the LIGO–Virgo band. Our constraint is a factor of 2 smaller that an estimate based on GW170817 being detected by searches that neglect eccentricity. However, we caution that we find significant prior dependence in our limits, suggesting that there is limited information in the signals. We note that other techniques used to constrain binary neutron star eccentricity without full parameter estimation may miss degeneracies in the waveform, and that for future signals, it will be important to perform full parameter estimation with accurate waveform templates. 

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