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arXiv 0902.0368gr-qc
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引力波天文探测问题的贝叶斯方法

A Bayesian Approach to the Detection Problem in Gravitational Wave Astronomy

Tyson B. Littenberg, Neil J. Cornish

摘要:

对来自引力波探测器的数据的分析可以分为三个阶段:搜索、表征和评估。对探测的评估--确定一个候选事件是天体物理学的起源还是仪器噪音造成的某种人为因素--是分析中的关键步骤。正在进行的数据分析,从地面探测器采用频率论的方法来检测问题。选择检测统计量,根据蒙特卡罗研究估计其背景水平和检测效率。这种方法将检测问题框定在无限的试验集合中,实际测量对应于这个假设集合的某种实现。在这里,我们探索一种替代方案,贝叶斯方法的检测问题,考虑先验信息和实际数据在手。我们特别关注的是用于实现贝叶斯分析的计算技术。我们发现,并行回火马尔可夫链蒙特卡罗(PTMCMC)算法是能够解决所有三个阶段的分析在一个连贯的框架。通过定位后验模态来发现信号,通过映射联合后验分布来表征模型参数,最后通过热力学积分计算模型证据。作为示范,我们考虑的检测问题之间的选择模型描述的数据作为仪器噪声,或仪器噪声加上信号从一个单一的紧凑的银河双星。的证据比,或贝叶斯因子,计算的PTMCMC算法被发现是在使用可逆跳马尔可夫链蒙特卡罗算法计算出的密切一致。

英文摘要:

The analysis of data from gravitational wave detectors can be divided into three phases: search, characterization, and evaluation. The evaluation of the detection - determining whether a candidate event is astrophysical in origin or some artifact created by instrument noise - is a crucial step in the analysis. The on-going analyses of data from ground based detectors employ a frequentist approach to the detection problem. A detection statistic is chosen, for which background levels and detection efficiencies are estimated from Monte Carlo studies. This approach frames the detection problem in terms of an infinite collection of trials, with the actual measurement corresponding to some realization of this hypothetical set. Here we explore an alternative, Bayesian approach to the detection problem, that considers prior information and the actual data in hand. Our particular focus is on the computational techniques used to implement the Bayesian analysis. We find that the Parallel Tempered Markov Chain Monte Carlo (PTMCMC) algorithm is able to address all three phases of the anaylsis in a coherent framework. The signals are found by locating the posterior modes, the model parameters are characterized by mapping out the joint posterior distribution, and finally, the model evidence is computed by thermodynamic integration. As a demonstration, we consider the detection problem of selecting between models describing the data as instrument noise, or instrument noise plus the signal from a single compact galactic binary. The evidence ratios, or Bayes factors, computed by the PTMCMC algorithm are found to be in close agreement with those computed using a Reversible Jump Markov Chain Monte Carlo algorithm.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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