Accelerated nested sampling with posterior repartitioning and $β$-flows for gravitational waves

Abstract

There is an ever-growing need in the gravitational wave community for fast and reliable inference methods, accompanied by an informative error bar. Nested sampling satisfies the last two requirements, but its computational cost can become prohibitive when using the most accurate waveform models. In this paper, we demonstrate the acceleration of nested sampling using a technique called posterior repartitioning. This method leverages nested sampling's unique ability to separate prior and likelihood contributions at the algorithmic level. Specifically, we define a `repartitioned prior' informed by the posterior from a low-resolution run. To construct this repartitioned prior, we use a $β$-flow, a novel type of conditional normalizing flow designed to better learn deep tail probabilities. $β$-flows are trained on the entire nested sampling run and conditioned on an inverse temperature $β$. Applying our methods to simulated and real binary black hole mergers, we demonstrate how they can reduce the number of likelihood evaluations required for a given evidence precision by up to an order of magnitude, enabling faster model comparison and parameter estimation. Furthermore, we highlight the robustness of using $β$-flows over standard normalizing flows for posterior repartitioning. Notably, $β$-flows are able to recover posteriors and evidences which are generally consistent with those from traditional nested sampling, even in cases where standard normalizing flows fail.