A Fisher matrix for gravitational-wave population inference

TL;DR

This paper develops a Fisher matrix formalism to estimate how precisely gravitational-wave population parameters can be inferred from multiple observations, accounting for uncertainties and selection effects.

Contribution

It introduces a general Fisher matrix framework for gravitational-wave population inference, applicable to various models and validated against Monte Carlo simulations.

Findings

Fisher matrix accurately predicts parameter estimation precision.

Framework accounts for measurement uncertainties and selection biases.

Validated with examples including black-hole mass distributions.

Abstract

We derive a Fisher matrix for the parameters characterising 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 increases. 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.