GWDALI: Derivative approximation for gravitational wave likelihoods

In the next decade, third-generation gravitational wave (GW) observatories, such as the Einstein Telescope and Cosmic Explorer, will begin operation, enabling the detection of compact object coalescences at unprecedented distances (up to z < 100). Analyzing these sources cosmologically necessitates GW parameter inference, which typically involves around 15 parameters for each detection—a process that is computationally intensive.

To address this challenge, we discuss the application of Derivative Approximation for Likelihoods (DALI) in gravitational wave and cosmological data analysis. DALI is a more time-efficient approach that incorporates higher-order terms in the Taylor expansion of likelihoods, which is particularly advantageous when the expected posterior distributions deviate from Gaussianity, rendering the Fisher Matrix approximation unreliable.

Such deviations often occur in the context of GW signals from compact binary coalescences, especially in cases of parameter degeneracies, such as the distance-inclination degeneracy. In this presentation, we explore the behavior of gravitational wave DALI-posteriors under various parameterizations of GW signals and demonstrate how their accuracy can be enhanced using automatic differentiation (autodiff).