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.

18 pages, 9 figures

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Cited by in corpus (6)

• Spatial and Spectral Characterization of the Gravitational-wave Background with the PTA Optimal Statistic
• Posterior predictive checking for gravitational-wave detection with pulsar timing arrays: I. The optimal statistic
• Choosing suitable noise models for nanohertz gravitational-wave astrophysics
• The NANOGrav 15 yr data set: Posterior predictive checks for gravitational-wave detection with pulsar timing arrays
• Rapid Construction of Joint Pulsar Timing Array Datasets: The Lite Method
• The NANOGrav 15 yr Data Set: Customized Chromatic Noise Models