### Abstract

Bayesian parameter estimation on gravitational waves from compact-binary coalescences (CBCs) typically requires millions of template waveform computations at different values of the parameters describing the binary. Sampling techniques such as Markov chain Monte Carlo and nested sampling evaluate likelihoods and, hence, compute template waveforms, serially; thus, the total computational time of the analysis scales linearly with that of template generation. Here we address the issue of rapidly computing the likelihood function of CBC sources with nonspinning components. We show how to efficiently compute the continuous likelihood function on the three-dimensional subspace of parameters on which it has a nontrivial dependence - the chirp mass, symmetric mass ratio and coalescence time - via interpolation. Subsequently, sampling this interpolated likelihood function is a significantly cheaper computational process than directly evaluating the likelihood; we report improvements in computational time of two to three orders of magnitude while keeping likelihoods accurate to 0.025%. Generating the interpolant of the likelihood function over a significant portion of the CBC mass space is computationally expensive but highly parallelizable, so the wall time can be very small relative to the time of a full parameter-estimation analysis.

Original language | English |
---|---|

Article number | 044074 |

Number of pages | 5 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 90 |

Issue number | 4 |

DOIs | |

Publication status | Published - 29 Aug 2014 |

### Keywords

- gravitational waves
- gravitational self-force
- black holes (astronomy)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*90*(4), [044074]. https://doi.org/10.1103/PhysRevD.90.044074

}

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 90, no. 4, 044074. https://doi.org/10.1103/PhysRevD.90.044074

**Rapidly evaluating the compact-binary likelihood function via interpolation.** / Smith, R. J.E.; Hanna, C.; Mandel, I.; Vecchio, A.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Rapidly evaluating the compact-binary likelihood function via interpolation

AU - Smith, R. J.E.

AU - Hanna, C.

AU - Mandel, I.

AU - Vecchio, A.

PY - 2014/8/29

Y1 - 2014/8/29

N2 - Bayesian parameter estimation on gravitational waves from compact-binary coalescences (CBCs) typically requires millions of template waveform computations at different values of the parameters describing the binary. Sampling techniques such as Markov chain Monte Carlo and nested sampling evaluate likelihoods and, hence, compute template waveforms, serially; thus, the total computational time of the analysis scales linearly with that of template generation. Here we address the issue of rapidly computing the likelihood function of CBC sources with nonspinning components. We show how to efficiently compute the continuous likelihood function on the three-dimensional subspace of parameters on which it has a nontrivial dependence - the chirp mass, symmetric mass ratio and coalescence time - via interpolation. Subsequently, sampling this interpolated likelihood function is a significantly cheaper computational process than directly evaluating the likelihood; we report improvements in computational time of two to three orders of magnitude while keeping likelihoods accurate to 0.025%. Generating the interpolant of the likelihood function over a significant portion of the CBC mass space is computationally expensive but highly parallelizable, so the wall time can be very small relative to the time of a full parameter-estimation analysis.

AB - Bayesian parameter estimation on gravitational waves from compact-binary coalescences (CBCs) typically requires millions of template waveform computations at different values of the parameters describing the binary. Sampling techniques such as Markov chain Monte Carlo and nested sampling evaluate likelihoods and, hence, compute template waveforms, serially; thus, the total computational time of the analysis scales linearly with that of template generation. Here we address the issue of rapidly computing the likelihood function of CBC sources with nonspinning components. We show how to efficiently compute the continuous likelihood function on the three-dimensional subspace of parameters on which it has a nontrivial dependence - the chirp mass, symmetric mass ratio and coalescence time - via interpolation. Subsequently, sampling this interpolated likelihood function is a significantly cheaper computational process than directly evaluating the likelihood; we report improvements in computational time of two to three orders of magnitude while keeping likelihoods accurate to 0.025%. Generating the interpolant of the likelihood function over a significant portion of the CBC mass space is computationally expensive but highly parallelizable, so the wall time can be very small relative to the time of a full parameter-estimation analysis.

KW - gravitational waves

KW - gravitational self-force

KW - black holes (astronomy)

UR - http://www.scopus.com/inward/record.url?scp=84908436170&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.90.044074

DO - 10.1103/PhysRevD.90.044074

M3 - Article

VL - 90

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 4

M1 - 044074

ER -