Extending the Fisher Information Matrix in Gravitational-wave Data Analysis

Understand

The Fisher information matrix (FM) plays an important role in forecasts and inferences in many areas of physics.

• While giving fast parameter estimation with the Gaussian likelihood approximation in the parameter space, the FM can only give the ellipsoidal posterior contours of parameters and lose the higher-order information beyond Gaussianity.
• We extend the FM in gravitational-wave (GW) data analysis using the Derivative Approximation for LIkelihoods (DALI), a method to expand the likelihood while keeping it positive definite and normalizable at every order, for more accurate forecasts and inferences.
• When applied to the two real GW events, GW150914 and GW170817, DALI can reduce the difference between FM approximation and the real posterior by 5 times in the best case.