Submitting Campus

Prescott

Department

Physics and Astronomy

Document Type

Article

Publication/Presentation Date

6-25-2010

Abstract/Description

In this paper we describe a new methodology to calculate analytically the error for a maximum likelihood estimate (MLE) for physical parameters from gravitational wave signals. All the existing literature focuses on the usage of the Cramer Rao Lower bounds (CRLB) as a mean to approximate the errors for large signal to noise ratios. We show here how the variance and the bias of an MLE estimate can be expressed instead in inverse powers of the signal to noise ratios where the first order in the variance expansion is the CRLB. As an application we compute the second order of the variance and bias for MLE of physical parameters from the inspiral phase of binary mergers and for noises of gravitational wave interferometers. We also compare the improved error estimate with existing numerical estimates. The value of the second order of the variance expansions allows to get error predictions closer to what is observed in numerical simulations. It also predicts correctly the necessary SNR to approximate the error with the CRLB and provides new insight on the relationship between waveform properties SNR and estimation errors. For example the timing match filtering becomes optimal only if the SNR is larger than the kurtosis of the gravitational wave spectrum.

Publication Title

Physical Review D

DOI

https://doi.org/10.1103/PhysRevD.81.124048

Publisher

American Physical Society

Grant or Award Name

National Science Foundation awards NSF0855567 and NSF0919034

Required Publisher’s Statement

Please view the publisher's version here

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