Fisher and DALI posterior approximations for testing gravity with gravitational waves
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}.
Related
- How general relativity stacks up: Testing gravity by coherently combining gravitational-wave observations
- The Impact of Inclination, Redshift, and Mass Ratio Selection on Cosmological Constraints from Bright Sirens Beyond Conventional Fisher Approximations
- Searching for gravitational wave echo with group equivariant neural posterior estimation
- Testing SALT Approximations with Numerical Radiative Transfer Code. II. Thermal and Microturbulent Line Broadening
- Fisher Information Velocity: A New Geometric Channel for Precision Glitch Identification in Gravitational-Wave Detectors
BibTeX
@misc{barbosa2026fisher,
title = {{Fisher and DALI posterior approximations for testing gravity with gravitational waves}},
author = {Felipe A. da Silva Barbosa and Davi C. Rodrigues and Josiel Mendonça Soares de Souza and Miguel Quartin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38399},
eprint = {2609.38399},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38399},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fisher and DALI posterior approximations for testing gravity with gravitational waves
AU - Felipe A. da Silva Barbosa
AU - Davi C. Rodrigues
AU - Josiel Mendonça Soares de Souza
AU - Miguel Quartin
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38399
UR - https://arxiv.org/abs/2609.38399
AB - 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}.
ER -