Geometrical aspects of parameter estimation of a stochastic gravitational wave background: Beyond the Fisher analysis
Geometrical aspects of parameter estimation of a stochastic gravitational wave background: Beyond the Fisher analysis
复制标题
DOI：
10.1103/physrevd.86.042002
复制
发表时间：
2012-06
影响因子：
5
通讯作者：
N. Seto;K. Kyutoku
中科院分区：
文献类型：
--
作者：
N. Seto;K. Kyutoku
最大似然法常用于引力波天文学中的参数估计。最近，Vallisneri 提出了一种有趣的方法来评估该方法预期的参数估计误差的分布。这种方法是对似然面的局部峰值进行统计分析，即使对于低信噪比的信号也能有效地工作。我们特别关注似然面的几何结构，遵循所提出的方法并推导出数据分析简化模型的公式，其中目标信号只有一个内在参数及其整体幅度。然后我们将我们的公式应用于随机引力波背景与幂律谱的相关分析。我们使用专门为两个 Advanced-LIGO 探测器进行相关分析而获得的数值结果来报告公式的定性趋势。
The maximum likelihood method is often used for parameter estimation in gravitational wave astronomy. Recently, an interesting approach was proposed by Vallisneri to evaluate the distributions of parameter estimation errors expected for the method. This approach is to statistically analyze the local peaks of the likelihood surface, and works efficiently even for signals with low signal-to-noise ratios. Focusing special attention to geometric structure of the likelihood surface, we follow the proposed approach and derive formulae for a simplified model of data analysis where the target signal has only one intrinsic parameter, along with its overall amplitude. Then we apply our formulae to correlation analysis of stochastic gravitational wave background with a power-law spectrum. We report qualitative trends of the formulae using numerical results specifically obtained for correlation analysis with two Advanced-LIGO detectors.