Multibanded Reduced Order Quadrature Techniques for Gravitational Wave Inference

TL;DR

The paper tackles the computational bottleneck in gravitational-wave parameter estimation posed by ROQ basis construction for long-duration signals. It introduces a multibanded ROQ construction strategy within PyROQ, enabling the basis search to be performed on frequency-band sliced data while preserving the accuracy of the ROQ likelihood. Applied to the IMRPhenomXAS_NRTidalV3 waveform in the subsolar-mass regime, the method achieves a 20–30% reduction in basis size and roughly a 6–13x speedup in construction time, with likelihood errors below $7\times 10^{-3}$ and no detectable biases in parameter estimation. This approach enables scalable ROQ for longer signals and paves the way for efficient analyses with future detectors.

Abstract

Reduced-order quadrature (ROQ) is commonly used to speed up parameter estimation in gravitational wave astronomy; however, the construction of ROQ bases can be computationally costly, particularly for longer duration signals. We propose a modified construction strategy based on PyROQ that accelerates this process by performing the basis search using multiband waveforms, without compromising the desired likelihood speed and accuracy. We use this altered method to construct a set of ROQs in the sub-solar mass range using the \texttt{IMRPhenomXAS\_NRTidalV3} waveform. We find a 20\% to 30\% decrease in basis size and a $\sim 10$ times decrease in basis construction time. We verify the altered method preserves the likelihood accuracy and mantains consitent parameter estimation results.

Figures (3)

• Figure 1: Illustration of a multibanded waveform in the frequency domain. The larger panel shows the full waveform, with the band boundaries marked using dashed vertical lines at $f = 100 \text{Hz}$, and $200\text{Hz}$. The multiple colors represent the different $\Delta f$ used across each band. The upper and lower smaller panels show a zoomed-in view of the same waveform at the $f = 100 \text{Hz}$ and $f = 200 \text{Hz}$ band boundaries, respectively, highlighting the change in $\Delta f$ across bands.
• Figure 2: The distributions of the likelihood errors between the full likelihood and the ROQ likelihood (red) and the multiband ROQ likelihood (green), respectively, for 6400 randomly drawn injected waveforms. The samples were drawn from the parameter space used to construct the 256s bases, as described in Section 2.3. All samples were found with likelihood errors less than $7\times 10^{-3}$.
• Figure 3: Corner plots comparing the posterior distributions between the standard PyROQ method (blue) and the multibanded construction method (orange). The parameter values for the injected waveform is given by the red lines. The dashed lines show the median, and $1\sigma$ credible interval.