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Abstract It is well known that the power spectrum is not able to fully characterize the statistical properties of non-Gaussian density fields. Recently, many different statistics have been proposed to extract information from non-Gaussian cosmological fields that perform better than the power spectrum. The Fisher matrix formalism is commonly used to quantify the accuracy with which a given statistic can constrain the value of the cosmological parameters. However, these calculations typically rely on the assumption that the sampling distribution of the considered statistic follows a multivariate Gaussian distribution. In this work, we follow Sellentin & Heavens and use two different statistical tests to identify non-Gaussianities in different statistics such as the power spectrum, bispectrum, marked power spectrum, and wavelet scattering transform (WST). We remove the non-Gaussian components of the different statistics and perform Fisher matrix calculations with theGaussianizedstatistics using Quijote simulations. We show that constraints on the parameters can change by a factor of ∼2 in some cases. We show with simple examples how statistics that do not follow a multivariate Gaussian distribution can achieve artificially tight bounds on the cosmological parameters when using the Fisher matrix formalism. We think that the non-Gaussian tests used in this work represent a powerful tool to quantify the robustness of Fisher matrix calculations and their underlying assumptions. We release the code used to compute the power spectra, bispectra, and WST that can be run on both CPUs and GPUs.
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A Fisher matrix for gravitational-wave population inference
ABSTRACT We derive a Fisher matrix for the parameters characterizing a population of gravitational-wave events. This provides a guide to the precision with which population parameters can be estimated with multiple observations, which becomes increasingly accurate as the number of events and the signal-to-noise ratio of the sampled events increase. The formalism takes into account individual event measurement uncertainties and selection effects, and can be applied to arbitrary population models. We illustrate the framework with two examples: an analytical calculation of the Fisher matrix for the mean and variance of a Gaussian model describing a population affected by selection effects, and an estimation of the precision with which the slope of a power-law distribution of supermassive black hole masses can be measured using extreme-mass-ratio inspiral observations. We compare the Fisher predictions to results from Monte Carlo analyses, finding very good agreement.
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- Award ID(s):
- 2207502
- PAR ID:
- 10390221
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 519
- Issue:
- 2
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- p. 2736-2753
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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