gwdali 1.0

Upgrade of GWDALI with automatic-differentiation

GWDALI Software

Software developed to perform parameter estimations of gravitational waves from compact objects coalescence (CBC) via Gaussian and Beyond-Gaussian approximation of GW likelihood [1,2]. The Gaussian approximation is related to Fisher Matrix, from which it is direct to compute the covariance matrix by inverting the Fisher Matrix [3]. GWDALI also deals with the not-so-infrequent cases of Fisher Matrix with zero-determinant, for instance, from Fisher Matrix inversion, the uncertainties of the luminosity distance diverges for small values of source inclinations (in contrast to what is shown in [4]). The Beyond-Gaussian approach uses the Derivative Approximation for LIkelihoods arXiv:1401.06892 (DALI) algorithm proposed in [5] and applied to gravitational waves in [6], whose model parameter uncertainties are estimated via Monte Carlo sampling but less costly than using the GW likelihood with no approximation. Check our papers in arXiv:2307.10154 and arXiv:2510.16955.

Installation

To install the software run the command below:

pip install gwdali

Requirements for LAL Waveforms and Autodiff

To be able to use LAL waveforms to compute GW polarizations/strains and to compute derivatives via automatic-differentiation (autodiff) install the packages lalsuite, lalsimulation, jax. It is recomended to use anaconda.

conda install lalsuite -c conda-forge
conda install lalsimulation -c conda-forge
conda install jax -c conda-forge

Documentation

Available in https://gwdali.readthedocs.io/en/latest/

Functionalities

• get_hphx(): It returns plus/cross polarizations in the frequency space (SPA);
• get_strain(): It retuns detector strains (signals) in the frequency space;
• get_SNR(): It retuns detector-network signal-to-noise ratios (individuals and net);
• draw_detectors(): It returns a world map showing the chosen detector network configuration;
• get_derivatives(): It returns detector signal derivatives;
• get_tensors(): It returns DALI tensors including Fisher matrix;
• Priors(): Check/Visualize priors to be used in Posterior evaluations;
• GWDALI(): Get MCMC/Fisher-Inversion Samples or Posterior-Grid Arrays;

Check https://gwdali.readthedocs.io/en/latest/examples.html for usage examples.

References

[1] de Souza, J. M. S., & Sturani, R. (2023). GWDALI: A Fisher-matrix based software for gravitational wave parameter-estimation beyond Gaussian approximation. Astronomy and Computing, 45, 100759.

[2] de Souza, J. M. S., & Quartin, M. (2025). On the use of the Derivative Approximation for Likelihoods for Gravitational Wave Inference. arXiv:2510.16955

[3] Finn, L. S., & Chernoff, D. F. (1993). Observing binary inspiral in gravitational radiation: One interferometer. Physical Review D, 47(6), 2198.

[4] de Souza, J. M. S., & Sturani, R. (2023). Luminosity distance uncertainties from gravitational wave detections of binary neutron stars by third generation observatories. Physical Review D, 108(4), 043027.

[5] Sellentin, E., Quartin, M., & Amendola, L. (2014). Breaking the spell of Gaussianity: forecasting with higher order Fisher matrices. Monthly Notices of the Royal Astronomical Society, 441(2), 1831-1840.

[6] Wang, Z., Liu, C., Zhao, J., & Shao, L. (2022). Extending the Fisher information matrix in gravitational-wave data analysis. The Astrophysical Journal, 932(2), 102.

Authors

• Josiel Mendonça Soares de Souza (developer)
• Riccardo Sturani (collaborator)
• Miguel Quartin (collaborator)

License

MIT License