Rapidly evaluating the compact binary likelihood function via interpolation

TL;DR

This paper introduces an interpolation-based method to rapidly evaluate the likelihood function for non-spinning compact binary coalescence gravitational wave sources, significantly reducing computation time while maintaining high accuracy.

Contribution

It presents a novel interpolation approach to efficiently compute the likelihood function over key parameters, enabling faster Bayesian analysis of gravitational wave data.

Findings

Achieves 100-300x speedup in likelihood evaluation

Maintains likelihood accuracy within 0.025%

Parallelizable method suitable for large parameter spaces

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 non-spinning components. We show how to efficiently compute the continuous likelihood function on the three-dimensional subspace of parameters on which it has a non-trivial 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.