Posterior predictive checking for gravitational-wave detection with pulsar timing arrays. II. Posterior predictive distributions and pseudo-Bayes factors
Abstract
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.
Copyright and License
© 2023 American Physical Society.
Acknowledgement
We thank Will Farr for discussions on posterior predictive checks in the LIGO context. Our analyses make use of enterprise [52,86], scipy [87], matplotlib [88], numpy [89], pandas [90], and seaborn [91]. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), supported by NSF award No. ACI-1548562, and specifically the Bridges-2 system at the Pittsburgh Supercomputing Center, supported by NSF award No. ACI-1928147. P. M. M., M. V., and K. C. were supported by the NANOGrav Physics Frontiers Center, National Science Foundation (NSF), Grant No. 2020265. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004).
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Additional details
- ISSN
- 2470-0029
- National Science Foundation
- OAC-1548562
- National Science Foundation
- OAC-1928147
- National Science Foundation
- PHY-2020265
- Jet Propulsion Laboratory
- California Institute of Technology
- National Aeronautics and Space Administration
- 80NM0018D0004
- Caltech groups
- LIGO, Astronomy Department, TAPIR, Walter Burke Institute for Theoretical Physics