December 2021 Uncertainty quantification of a computer model for binary black hole formation
Luyao Lin, Derek Bingham, Floor Broekgaarden, Ilya Mandel
Author Affiliations +
Ann. Appl. Stat. 15(4): 1604-1627 (December 2021). DOI: 10.1214/21-AOAS1484


In this paper, a fast and parallelizable method based on Gaussian processes (GPs) is introduced to emulate computer models that simulate the formation of binary black holes (BBHs) through the evolution of pairs of massive stars. Two obstacles that arise in this application are the a priori unknown conditions of BBH formation and the large scale of the simulation data. We address them by proposing a local emulator which combines a GP classifier and a GP regression model. The resulting emulator can also be utilized in planning future computer simulations through a proposed criterion for sequential design. By propagating uncertainties of simulation input through the emulator, we are able to obtain the distribution of BBH properties under the distribution of physical parameters.

Funding Statement

IM is a recipient of the Australian Research Council Future Fellowship FT190100574. IM acknowledges support from the Australian Research Council Centre of Excellence for Gravitational Wave Discovery (OzGrav), through project number CE17010000. This work was also supported by EPSRC grant no. EP/R014604/1 and a Natural Sciences and Engineering Research Council of Canada Discovery Grant.


We thank Jim Barrett and Simon Stevenson for contributions to early testing data and discussions. Simulations in this paper made use of the COMPAS rapid binary population synthesis code, which is freely available at The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, for support and hospitality during the program “Uncertainty quantification for complex systems: theory and methodologies” and also the Statistical and Applied Mathematical Sciences Institute’s program on Statistical, Mathematical and Computational Methods for Astronomy where work on this paper was initially undertaken. IM acknowledges affiliation with the Australian Research Council Centre of Excellence for Gravitational Wave Discovery (OzGrav), and Birmingham Institute for Gravitational Wave Astronomy and School of Physics and Astronomy at University of Birmingham.


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Luyao Lin. Derek Bingham. Floor Broekgaarden. Ilya Mandel. "Uncertainty quantification of a computer model for binary black hole formation." Ann. Appl. Stat. 15 (4) 1604 - 1627, December 2021.


Received: 1 January 2021; Revised: 1 May 2021; Published: December 2021
First available in Project Euclid: 21 December 2021

MathSciNet: MR4355068
zbMATH: 1498.62342
Digital Object Identifier: 10.1214/21-AOAS1484

Keywords: computer experiments , local approximate GP , sequential design , surrogate model

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.15 • No. 4 • December 2021
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