GWDALI Software (version 1.0)

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 \(\sigma_{d_L}(\iota)\) diverges for small values of source inclinations \(\iota\) (in contrast to what is shown in [4]). The Beyond-Gaussian approach uses the Derivative Approximation for LIkelihoods (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.

• Published Paper (Astronomy and Computing)

• pypi page

• github page

Installation

To install the software run the command below:

git clone https://github.com/jmsdsouzaPhD/GWDALI.git
cd GWDALI/package/
pip install -e .

Contents:

• API Reference
  • Main Interface
  • Waveforms
  • Derivatives
  • DALI Tensors
  • Check Priors
  • Detector Utilities
• Derivative Approximation for LIkelihood (DALI)
• Priors
  • Default Priors
  • Make your own prior
• GW Source Characterization
  • Mass Parameterizations
  • Distance Parameterizations
  • Inclination Parameterizations
  • Spin Parameterizations
  • Extrinsic Parameters
  • Example: Source Dictionary Construction
  • Sky Localization
• Detectors (Position/Orientation/Shape)
  • Detectors Sensitivity
• Examples
  • Jupyter Notebooks (.ipynb)
  • Top-Down Python Codes (.py)
• List of papers using GWDALI
• Citation
  • Release papers
• License
• About the Author

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.