Bayesian cross validation for gravitationalwave searches in pulsartiming array data
Abstract
Gravitationalwave data analysis demands sophisticated statistical noise models in a bid to extract highly obscured signals from data. In Bayesian model comparison, we choose among a landscape of models by comparing their marginal likelihoods. However, this computation is numerically fraught and can be sensitive to arbitrary choices in the specification of parameter priors. In Bayesian cross validation, we characterize the fit and predictive power of a model by computing the Bayesian posterior of its parameters in a training data set, and then use that posterior to compute the averaged likelihood of a different testing data set. The resulting crossvalidation scores are straightforward to compute; they are insensitive to prior tuning; and they penalize unnecessarily complex models that overfit the training data at the expense of predictive performance. In this article, we discuss cross validation in the context of pulsartimingarray data analysis, and we exemplify its application to simulated pulsar data (where it successfully selects the correct spectral index of a stochastic gravitationalwave background), and to a pulsar data set from the NANOGrav 11yr release (where it convincingly favours a model that represents a transient feature in the interstellar medium). We argue that cross validation offers a promising alternative to Bayesian model comparison, and we discuss its use for gravitationalwave detection, by selecting or refuting models that include a gravitationalwave component.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 August 2019
 DOI:
 10.1093/mnras/stz1537
 arXiv:
 arXiv:1904.05355
 Bibcode:
 2019MNRAS.487.3644W
 Keywords:

 gravitational waves;
 methods: statistical;
 pulsars: general;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 7 pages, 4 figures. Submitted to MNRAS