Accelerated Gravitational Wave Parameter Estimation with Reduced Order Modeling

Inferring the astrophysical parameters of coalescing compact binaries is a key science goal of the upcoming advanced LIGO-Virgo gravitational-wave detector network and, more generally, gravitational-wave astronomy. However, current approaches to parameter estimation for these detectors require computationally expensive algorithms. Therefore, there is a pressing need for new, fast, and accurate Bayesian inference techniques. In this Letter, we demonstrate that a reduced order modeling approach enables rapid parameter estimation to be performed. By implementing a reduced order quadrature scheme within the LIGO Algorithm Library, we show that Bayesian inference on the 9-dimensional parameter space of nonspinning binary neutron star inspirals can be sped up by a factor of $\sim 30$ for the early advanced detectors’ configurations (with sensitivities down to around 40 Hz) and $\sim 70$ for sensitivities down to around 20 Hz. This speedup will increase to about 150 as the detectors improve their low-frequency limit to 10 Hz, reducing to hours analyses which could otherwise take months to complete. Although these results focus on interferometric gravitational wave detectors, the techniques are broadly applicable to any experiment where fast Bayesian analysis is desirable.

Figure 1

Top: length $L$ (red dots) of a typical binary neutron star inspiral waveform, with the solid black curve connecting this data implied by the fit (7). Middle: number of reduced basis waveforms (red crosses), with the solid black curve given by the fit (8). Bottom: speedup implied by operation counts, as given by Eq. (9).

Figure 2

Probability density function for the chirp mass ${\mathcal{M}}_c$ and symmetric mass ratio $\eta$ of a simulated event in LIGO-Virgo data. In green as obtained in $\sim 30\mathrm{h}$ by the standard likelihood, and in blue as obtained in 1 h with the ROQ. The injection values are in red, and are listed in Table 1. The overlap region of the sets of PDFs is the hatched region. Plotting based on [29].