Fisher vs. Bayes：用eLISA对大质量黑洞双星和高红移的参数估计技术的比较
Fisher vs. Bayes : A comparison of parameter estimation techniques for massive black hole binaries to high redshifts with eLISA
摘要：
大质量黑洞双星是未来eLISA天文台的主要引力波源。这些高红移源的探测和参数估计将为种子黑洞的形成机制以及大质量黑洞及其宿主星系在宇宙时间中的演化提供宝贵的信息。在过去的二十年里，Fisher信息矩阵一直是GW参数估计的标准工具。然而，最近的研究质疑使用Fisher矩阵方法的有效性。例如，Fisher矩阵方法有时在诸如亮度距离和天空位置的参数的估计中预测$\geq100\%$的误差。随着计算能力的提高，贝叶斯推断开始取代参数估计研究中的Fisher矩阵近似。在这项工作中，我们进行贝叶斯推断分析位于红移之间的$0.1\leq z\leq 13.2$的120个来源，并比较结果与Fisher矩阵分析。Fisher矩阵的结果表明，对于这种特殊的源选择，eLISA将无法定位在红移为$z\lesssim6$的源。相比之下，贝叶斯推断提供了有限的误差估计的所有来源的研究，并表明，我们可以建立所有来源的最小最近距离。这项研究进一步预测，我们应该能够用eLISA，在至少$z\leq13$的红移下，预测$\lesssim 1\%$的啁啾质量的最大误差，$\lesssim20\%$的约化质量，2小时的合并时间，以及$z\sim5$的红移，最大误差为$\sim60$度的源倾斜。
英文摘要：
Massive black hole binaries are the primary source of gravitational waves (GW) for the future eLISA observatory. The detection and parameter estimation of these sources to high redshift would provide invaluable information on the formation mechanisms of seed black holes, and on the evolution of massive black holes and their host galaxies through cosmic time. The Fisher information matrix has been the standard tool for GW parameter estimation in the last two decades. However, recent studies have questioned the validity of using the Fisher matrix approach. For example, the Fisher matrix approach sometimes predicts errors of $\geq100\%$ in the estimation of parameters such as the luminosity distance and sky position. With advances in computing power, Bayesian inference is beginning to replace the Fisher matrix approximation in parameter estimation studies. In this work, we conduct a Bayesian inference analysis for 120 sources situated at redshifts of between $0.1\leq z\leq 13.2$, and compare the results with those from a Fisher matrix analysis. The Fisher matrix results suggest that for this particular selection of sources, eLISA would be unable to localize sources at redshifts of $z\lesssim6$. In contrast, Bayesian inference provides finite error estimations for all sources in the study, and shows that we can establish minimum closest distances for all sources. The study further predicts that we should be capable with eLISA, out to a redshift of at least $z\leq13$, of predicting a maximum error in the chirp mass of $\lesssim 1\%$, the reduced mass of $\lesssim20\%$, the time to coalescence of 2 hours, and to a redshift of $z\sim5$, the inclination of the source with a maximum error of $\sim60$ degrees.
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