引力波天文学中贝叶斯模型选择技术的检验
Tests of Bayesian Model Selection Techniques for Gravitational Wave Astronomy
摘要：
引力波资料的分析涉及到许多模型选择问题。最重要的例子是在仅与仪器噪声一致的数据或与仪器噪声和引力波信号一致的数据之间进行选择的检测问题。对地面引力波探测器数据的分析大多采用经典统计学方法进行，并采用Neyman-Pearson准则等方法进行模型选择。未来的空间探测器，如\emph{Laser Interferometer Space Antenna}（LISA），预计将产生丰富的数据流，包含来自数百万个源的信号。确定可解析的源的数量，以及每个源的最适当的描述构成了一个具有挑战性的模型选择问题，该问题可以在贝叶斯框架中得到最好的解决。LISA的一个重要来源是我们银河系中数百万个低质量双星系统，其中数万个是可以探测到的。不仅源的数量是未知的，而且建模波形所需的参数的数量也是未知的。例如，一个重要的可分辨星系双星的子集将显示轨道频率的演变，而一个较小的数字将有可测量的偏心率。在贝叶斯模型选择方法中，需要计算竞争模型之间的贝叶斯因子。在这里，我们将探讨各种方法来计算贝叶斯因子的背景下，确定银河双星可测量的频率演变。探索的方法包括反向跳马尔可夫链蒙特卡罗（RJMCMC）算法，萨维奇-迪基密度比，施瓦茨-贝叶斯信息准则（BIC），和拉普拉斯近似模型的证据。我们发现所有的方法之间的良好协议。
英文摘要：
The analysis of gravitational wave data involves many model selection problems. The most important example is the detection problem of selecting between the data being consistent with instrument noise alone, or instrument noise and a gravitational wave signal. The analysis of data from ground based gravitational wave detectors is mostly conducted using classical statistics, and methods such as the Neyman-Pearson criteria are used for model selection. Future space based detectors, such as the \emph{Laser Interferometer Space Antenna} (LISA), are expected to produced rich data streams containing the signals from many millions of sources. Determining the number of sources that are resolvable, and the most appropriate description of each source poses a challenging model selection problem that may best be addressed in a Bayesian framework. An important class of LISA sources are the millions of low-mass binary systems within our own galaxy, tens of thousands of which will be detectable. Not only are the number of sources unknown, but so are the number of parameters required to model the waveforms. For example, a significant subset of the resolvable galactic binaries will exhibit orbital frequency evolution, while a smaller number will have measurable eccentricity. In the Bayesian approach to model selection one needs to compute the Bayes factor between competing models. Here we explore various methods for computing Bayes factors in the context of determining which galactic binaries have measurable frequency evolution. The methods explored include a Reverse Jump Markov Chain Monte Carlo (RJMCMC) algorithm, Savage-Dickie density ratios, the Schwarz-Bayes Information Criterion (BIC), and the Laplace approximation to the model evidence. We find good agreement between all of the approaches.
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