论文标题
重力波种群推断的Fisher矩阵
A Fisher matrix for gravitational-wave population inference
论文作者
论文摘要
我们得出一个用于表征重力波事件群体的参数的Fisher矩阵。这提供了一个指南，可以通过多个观测值估算人口参数的精度，随着事件的数量和采样事件的信噪比增加，该观察变得越来越准确。形式主义考虑了个别事件测量不确定性和选择效果，可以应用于任意人口模型。我们用两个示例说明了框架：用于描述受选择效果影响的人群的高斯模型的均值和差异的Fisher矩阵的分析计算，以及可以使用极端的质量激气式启发性观察来测量超级质量黑洞质量斜率的斜率。我们将Fisher的预测与蒙特卡洛分析的结果进行了比较，发现了很好的一致性。
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.
