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arXiv · 2609.38399

Fisher and DALI posterior approximations for testing gravity with gravitational waves

Felipe A. da Silva Barbosa·Davi C. Rodrigues·Josiel Mendonça Soares de Souza·Miguel Quartin
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Abstract

We investigate the accuracy and computational efficiency of posterior approximations for gravitational-wave (GW) parameter estimation based on Fisher Matrix and its higher-order extension, the Derivative Approximation for LIkelihoods (DALI), in the context of tests of General Relativity using parameterized deviations in the inspiral waveforms (the TIGER formalism). We adopt the \texttt{IMRPhenomD} waveform and compare the exact posterior sampling to the following approximations in increasing order of complexity: the traditional Fisher Matrix, the Fisher sampling (singlet-DALI), the doublet-DALI and the triplet-DALI. We find that both singlet and doublet-DALI are significantly faster than the exact posterior by factors between 20 and 1000, depending on the inspiral SNRs -- larger gains correspond to larger SNRs. These gains are considerably larger for more complete waveforms, such as \texttt{IMRPhenomHM}. To evaluate the accuracy of the approximations, we use Jensen-Shannon divergence. We conclude that both singlet and doublet-DALI systematically improves over the standard Fisher Matrix approximation, while triplet-DALI shows large variability, limiting its practical advantage. We also introduce a code with a new implementation of Fisher and DALI analysis (Symbolic DALI, \texttt{SymDALI}) which computes derivatives symbolically via \textit{Wolfram Language}.

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Felipe A. da Silva Barbosa, Davi C. Rodrigues, Josiel Mendonça Soares de Souza, Miguel Quartin. 2026-09-29. Fisher and DALI posterior approximations for testing gravity with gravitational waves. https://arxiv.org/abs/2609.38399

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