Geometrical Aspects on Parameter estimation of stochastic gravitational wave background: beyond the Fisher analysis

TL;DR

This paper extends the geometric analysis of likelihood surfaces for parameter estimation in gravitational wave background studies, providing new formulae applicable to low signal-to-noise scenarios and stochastic background correlation analysis.

Contribution

It derives simplified geometric formulae for parameter estimation errors and applies them to stochastic gravitational wave background correlation analysis.

Findings

Qualitative trends of estimation errors with low SNR

Effective geometric formulae for stochastic background analysis

Numerical validation with Advanced-LIGO detectors

Abstract

The maximum likelihood method is often used for parameter estimation in gravitational wave astronomy. Recently, an interesting approach was proposed by Vallisneri to evaluate the distributions of parameter estimation errors expected for the method. This approach is to statistically analyze the local peaks of the likelihood surface, and works efficiently even for signals with low signal-to-noise ratios. Focusing special attention to geometric structure of the likelihood surface, we follow the proposed approach and derive formulae for a simplified model of data analysis where the target signal has only one intrinsic parameter, along with its overall amplitude. Then we apply our formulae to correlation analysis of stochastic gravitational wave background with a power-law spectrum. We report qualitative trends of the formulae using numerical results specifically obtained for correlation analysis with two Advanced-LIGO detectors.