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

Install GWDALI from PyPI with

pip install gwdali

This command also installs the required Python dependencies, including JAX.

Additional Requirements

GWDALI depends on JAX for automatic differentiation, JIT-accelerated likelihood evaluations, and several internal numerical routines.

For most systems, pip install gwdali installs JAX automatically.

If the JAX installation through pip fails (for example on older CPUs without AVX support or on specific hardware platforms), install JAX manually following the official JAX installation instructions or using conda-forge, and then install GWDALI.

conda install -c conda-forge jax

If you intend to use LAL waveform models, install LALSuite as well:

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

The waveform models implemented directly in GWDALI do not require LALSuite.

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 returns detector strains (signals) in the frequency space;
• get_SNR(): It returns 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(): Returns MCMC samples, 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. (2026). On the use of the Derivative Approximation for Likelihoods for gravitational wave inference. Journal of Cosmology and Astroparticle Physics, 2026(05), 101.

[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

BSD 3-Clause License

Copyright (c) 2026, Josiel Mendonça Soares de Souza

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Aknowledgements

This work was partialy suported by:

• Coordenação de Aperfeiçoamente de Pessoal de Ensino Superior (CAPES);
• Fundação Carlos Chargas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ);
• Fundação de Amparo à Pesquisa e Inovação do Espírito Santo (FAPES);

The authors also thank Davi Rodrigues (UFES) for usefull discussions.