GWDALI: A Fisher-matrix based software for gravitational wave parameter-estimation beyond Gaussian approximation

TL;DR

GWDALI is a Python software tool that enhances gravitational wave parameter estimation by incorporating likelihood derivatives to go beyond traditional Fisher-matrix approximations, especially useful when the Fisher matrix is non-invertible.

Contribution

It introduces a novel Fisher-matrix based software that assesses parameter uncertainties beyond Gaussian approximation using the DALI method.

Findings

Effective in estimating parameter uncertainties beyond Fisher approximation.

Useful when the Fisher matrix is non-invertible.

Demonstrates comparison between exact likelihood and derivative approximations.

Abstract

We introduce GWDALI, a new Fisher-matrix, python based software that computes likelihood gradients to forecast parameter-estimation precision of arbitrary network of terrestrial gravitational wave detectors observing compact binary coalescences. The main new feature with respect to analogous software is to assess parameter uncertainties beyond Fisher-matrix approximation, using the derivative approximation for Likelihood (DALI). The software makes optional use of the LSC algorithm library LAL and the stochastic sampling algorithm Bilby, which can be used to perform Monte-Carlo sampling of exact or approximate likelihood functions. As an example we show comparison of estimated precision measurement of selected astrophysical parameters for both the actual likelihood, and for a variety of its derivative approximations, which turn out particularly useful when the Fisher matrix is not invertible.