Parameter estimation from Gravitational waves generated by non-spinning binary black holes with laser interferometers: beyond the Fisher information

TL;DR

This paper introduces a new analytical frequentist method to estimate errors in gravitational wave parameter measurements from non-spinning binary black holes, extending beyond traditional Fisher information approaches.

Contribution

It applies a power expansion technique to analyze bias and covariance of the maximum likelihood estimates, revealing new features and limitations of existing methods.

Findings

Bias becomes dominant in high-mass systems (200M and above).

Predictions are sensitive to secondary lobes of the likelihood distribution.

Conditions for the validity of the Cramer Rao Lower Bound are discussed.

Abstract

In this paper we apply to gravitational waves from non-spinning binary systems a recently intro- duced frequentist methodology to calculate analytically the error for a maximum likelihood estimate (MLE) of physical parameters. While existing literature focuses on using the Cramer Rao Lower bound (CRLB) and Monte Carlo simulations, we use a power expansion of the bias and covariance in inverse powers of the signal to noise ratio. The use of higher order derivatives of the likelihood function in the expansions makes the prediction also sensitive to the secondary lobes of the MLE probability distribution. We discuss conditions for validity of the CRLB and predict new features in regions of the parameter space currently not explored. For example, we see how the bias can become the most important contributor to the parameters' errors for high mass systems (200M and above).