Posterior predictive checking for gravitational-wave detection with pulsar timing arrays: II. Posterior predictive distributions and pseudo Bayes factors

TL;DR

This paper develops posterior predictive checks to evaluate models in pulsar timing array data for nanoHertz gravitational wave detection, helping identify model misspecification and improve detection confidence.

Contribution

It introduces novel posterior predictive checks based on Fourier coefficients, correlation patterns, and residuals for assessing model fit in gravitational wave detection.

Findings

Checks can identify deviations from the power-law spectral shape.

Checks can detect incorrect angular correlation patterns.

Likelihoods under different models help quantify detection significance.

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.