Application of the effective Fisher matrix to the frequency domain inspiral waveforms

Abstract

The Fisher matrix (FM) has been generally used to predict the accuracy of the gravitational wave parameter estimation. Although the limitation of the FM has been well known, it is still mainly used due to its very low computational cost compared to the Monte Carlo simulations. Recently, Rodriguez et al. [Phys. Rev. D 88, 084013 (2013)] performed Markov chain Monte Carlo (MCMC) simulations using a frequency domain inspiral waveform model (TaylorF2) for nonspinning binary systems with total masses M ≤ 20M ⊙ , they found systematic differences between the predictions from FM and MCMC for M > 10M ⊙ . On the other hand, an effective Fisher matrix (eFM) was recently introduced by Cho et al. [Phys. Rev. D 87, 24004 (2013)]. The eFM is a semi-analytic approach to the standard FM, in which the derivative is taken of a quadratic function fitted to the local overlap surface. In this work, we apply the eFM method to the TaylorF2 waveform for nonspinning binary systems with a moderately high signal to noise ratio (SNR ∼ 15) and find that the eFM can well reproduce the MCMC error bounds in Rodriguez et al. even for high masses. By comparing the eFM standard deviation directly with the 1-σ confidence interval of the marginalized overlap that approximates the MCMC posterior distribution, we show that the eFM can be acceptable in all mass regions for the estimation of the MCMC error bounds. We also investigate the dependence on the signal strength.

Reconstructing phenomenological distributions of compact binaries via gravitational wave observations

“…We generate samples from this distribution via Monte Carlo techniques. We evaluate the approximate Fisher matrix Γ using the effective Fisher technique [55,82,104], applied to a nonprecessing binary waveform model assigned the same values of M c , η, χ eff (i.e., via χ 1,z = χ 2,z = χ eff ). This approximate posterior distribution has several distinct advantages.…”

Gravitational wave searches for aligned-spin binary neutron stars using nonspinning templates

“…In order to describe aligned-spin binary systems in circular orbits, the wave function should incorporate five extrinsic parameters (luminosity distance of the binary, two angles defining the sky position of the binary with respect to the detector, orbital inclination, and wave polarization), two arbitrary constants (coalescence time t c and coalescence phase φ c ), and four intrinsic parameters (two masses and two spins). On the other hand, the extrinsic parameters only scale the wave am-arXiv:1708.00426v1 [gr-qc] 1 Aug 2017 plitude, hence do not affect our analysis [27]. Therefore, we do not consider those extrinsic parameters in this work.…”

Synergy between ground and space based gravitational wave detectors. Part II: Localisation

“…Note that the Fisher matrix formalism is limited to high SNR cases (see [30][31][32][33][34] for case studies where the Fisher matrix formalism fails). In spite of its limitations, the Fisher matrix method is the simplest and one of the most inexpensive ways to infer parameter uncertainties from future surveys.…”