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Inferring the Properties of a Population of Compact Binaries in Presence of Selection Effects

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Handbook of Gravitational Wave Astronomy

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Abstract

Shortly after a new class of objects is discovered, the attention shifts from the properties of the individual sources to the question of their origin: do all sources come from the same underlying population, or several populations are required? What are the properties of these populations? As the detection of gravitational waves is becoming routine and the size of the event catalog increases, finer and finer details of the astrophysical distribution of compact binaries are now within our grasp. This chapter presents a pedagogical introduction to the main statistical tool required for these analyses: hierarchical Bayesian inference in the presence of selection effects. All key equations are obtained from first principles, followed by two examples of increasing complexity. Although many remarks made in this chapter refer to gravitational-wave astronomy, the write-up is generic enough to be useful to researchers and graduate students from other fields.

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Acknowledgements

We thank Sylvia Biscoveanu for a critical reading of an early draft of these notes, as wells as Emanuele Berti, Maya Fishbach, Max Isi, and Ken Ng for long and illuminating discussions. We thank Nancy Aggarwal and Peter Couvares for useful comments. S.V. acknowledges the support of the National Science Foundation though PHY-2045740, the LIGO Laboratory and the MIT physics department through the Solomon Buchsbaum Research Fund. D.G is supported by European Union’s H2020 ERC Starting Grant No. 945155-GWmining, Cariplo Foundation Grant No. 2021-0555, and Leverhulme Trust Grant No. RPG-2019-350. LIGO was constructed by the California Institute of Technology and Massachusetts Institute of Technology with funding from the National Science Foundation and operates under cooperative agreement PHY-0757058. We acknowledge use of iPython [86], Matplotlib [87, 88], NumPy [89], SciPy [90], emcee [91], and SeaBorn [92]. This is LIGO Document P2000231. S.R.T is supported by National Science Foundation grants AST-2007993, PHY-2020265, PHY-2146016. S.R.T also acknowledges support from a Vanderbilt University College of Arts & Science Dean’s Faculty Fellowship.

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Authors and Affiliations

  1. Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA, USA

    Salvatore Vitale

  2. LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA, USA

    Salvatore Vitale

  3. Dipartimento di Fisica “G. Occhialini”, Universitá degli Studi di Milano-Bicocca, Piazza della Scienza, Milano, Italy

    Davide Gerosa

  4. INFN, Sezione di Milano-Bicocca, Piazza della Scienza, Milano, Italy

    Davide Gerosa

  5. School of Physics and Astronomy, Institute for Gravitational Wave Astronomy, University of Birmingham, Birmingham, UK

    Davide Gerosa

  6. Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA

    Will M. Farr

  7. Center for Computational Astrophysics, Flatiron Institute, New York, NY, USA

    Will M. Farr

  8. Department of Physics and Astronomy, Vanderbilt University, Nashville, TN, USA

    Stephen R. Taylor

Authors
  1. Salvatore Vitale
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  2. Davide Gerosa
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  3. Will M. Farr
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  4. Stephen R. Taylor
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Corresponding author

Correspondence to Salvatore Vitale .

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Editors and Affiliations

  1. Department of Physics, Fudan University, Shanghai, China

    Cosimo Bambi

  2. Université de Paris and European Gravitational Observatory, Paris, France

    Stavros Katsanevas

  3. Institute for Astronomy and Astrophysics Eberhard Karls, University of Tübingen, Tübingen, Germany

    Konstantinos D. Kokkotas

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Vitale, S., Gerosa, D., Farr, W.M., Taylor, S.R. (2022). Inferring the Properties of a Population of Compact Binaries in Presence of Selection Effects. In: Bambi, C., Katsanevas, S., Kokkotas, K.D. (eds) Handbook of Gravitational Wave Astronomy. Springer, Singapore. https://doi.org/10.1007/978-981-16-4306-4_45

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