Posterior predictive checking for gravitational-wave detection with pulsar timing arrays. II. Posterior predictive distributions and pseudo-Bayes factors
Posterior predictive checking for gravitational-wave detection with pulsar timing arrays. II. Posterior predictive distributions and pseudo-Bayes factors
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DOI：
10.1103/physrevd.108.123008
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发表时间：
2023-06
影响因子：
5
通讯作者：
P. Meyers;K. Chatziioannou;M. Vallisneri;A. J. Chua
中科院分区：
文献类型：
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作者：
P. Meyers;K. Chatziioannou;M. Vallisneri;A. J. Chua
通过脉冲星计时阵列检测纳赫兹引力波取决于识别一个共同的随机过程，该过程以相关的方式影响天空中的所有脉冲星。在存在影响脉冲到达时间的其他确定性和随机过程的情况下，检测声明必须附有对用于描述数据的各种物理或现象学模型的详细评估。在本研究中，我们提出后验预测检查作为模型检查工具，它依赖于模型对新数据的预测性能。我们根据模型的不同组成部分（即随机过程的傅里叶系数、相关模式和时序残差）推导并研究预测检查。我们评估我们的检查识别模拟数据集中模型错误指定的能力。我们发现它们可以准确地标记偏离常见幂律模型的随机过程谱形状以及不显示预期角度相关模式的随机过程。在关于相关模式的不同假设下导出的后验预测可能性可以进一步用于建立检测显着性。在从不同脉冲星定时数据集进行纳赫兹引力波检测的时代，此类测试是评估数据一致性和支持天体物理推理的重要工具。
The detection of nanoHertz gravitational waves through pulsar timing arrays hinges on identifying a common stochastic process affecting all pulsars in a correlated way across the sky. In the presence of other deterministic and stochastic processes affecting the time-of-arrival of pulses, a detection claim must be accompanied by a detailed assessment of the various physical or phenomenological models used to describe the data. In this study, we propose posterior predictive checks as a model-checking tool that relies on the predictive performance of the models with regards to new data. We derive and study predictive checks based on different components of the models, namely the Fourier coefficients of the stochastic process, the correlation pattern, and the timing residuals. We assess the ability of our checks to identify model misspecification in simulated datasets. We find that they can accurately flag a stochastic process spectral shape that deviates from the common power-law model as well as a stochastic process that does not display the expected angular correlation pattern. Posterior predictive likelihoods derived under different assumptions about the correlation pattern can further be used to establish detection significance. In the era of nanoHertz gravitational wave detection from different pulsar-timing datasets, such tests represent an essential tool in assessing data consistency and supporting astrophysical inference.