Use and abuse of the Fisher information matrix in the assessment of gravitational-wave parameter-estimation prospects

By Michele Vallisneri. 2007

402 citations recorded by the source corpus.

The Fishermatrix formalism is used routinely in the literature on gravitational-wave detection to characterize the parameter-estimation performance of gravitational-wave measurements, given parametrized models of the waveforms, and assuming detector noise of known colored Gaussian distribution. Unfortunately, the Fisher matrix can be a poor predictor of the amount of information obtained from typical observations, especially for waveforms with several parameters and relatively low expected signal-to-noise ratios (SNR), or for waveforms depending weakly on one or more parameters, when their priors are not taken into proper consideration. In this paper I discuss these pitfalls; show how they occur, even for relatively strong signals, with a commonly used template family for binary-inspiral waveforms; and describe practical recipes to recognize them and cope with them. Specifically, I answer the following questions: (i) What is the significance of (quasi-)singular Fisher matrices, and how must we deal with them? (ii) When is it necessary to take into account prior probability distributions for the source parameters? (iii) When is the signal-to-noise ratio high enough to believe the Fisher-matrix result? In addition, I provide general expressions for the higher-order, beyond-Fisher-matrix terms in the 1/SNR expansions for the expected parameter accuracies.

Subfields: Astronomy and Astrophysics, Geophysics

View Paper: https://www.semanticscholar.org/paper/c3bda9cd810f549f52b8afd30e588ecbcccf1311

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Citations in the corpus

Physics, Astrophysics and Cosmology with Gravitational Waves (2009, methodology): “Section 4 also compares the sensitivity of the antennas with the strengths of astronomical sources and expected signal-to-noise ratios (SNRs).”
Extracting distribution parameters from multiple uncertain observations with selection biases (2018, background): “…covariance matrix at lower values of ρ where the linear signal approximation breaks down, the loglikelihood ceases to be well approximated by a quadratic (Vallisneri 2008), and the prior constraints on variables strongly correlated with η, such as the spin parameters, become increasingly important.”
Ultrahigh precision cosmology from gravitational waves (2009, neutral): “4372 [56] M. Vallisneri 2008, Phys.”
Constraining Formation Models of Binary Black Holes with Gravitational-wave Observations (2017, background): “Note that the convergence rate varies depending both on the injected value of β and the injected kick prescription. spin and symmetric mass ratio (see, e.g. Vallisneri 2008; Rodriguez et al. 2013; O’Shaughnessy et al. 2014).”
Predicting the LISA white dwarf binary population in the Milky Way with cosmological simulations (2019, methodology): “The Fisher matrix is only an approximation with well-publicized shortcomings (Vallisneri 2008) but, similar to the argument for the hierarchical search method, a more robust error analysis (e.g., using stochastic sampling methods) requires prohibitive computationally resources for the scope of this…”