Pulsar Timing Arrays Require Hierarchical Models

Pulsar Timing Array projects have found evidence of a stochastic background of gravitational waves (GWB) using data from an ensemble of pulsars. In the literature, minimal assumptions are made about the signal and noise processes that affect data from these pulsars, such as pulsar spin noise. These assumptions are encoded as uninformative priors in Bayesian searches, though Frequentist approaches make similar assumptions. Uninformative priors are not suitable for (noise) properties of pulsars in an ensemble, and they bias estimates of model parameters such as gravitational-wave signal parameters. Both Frequentist and Bayesian searches are affected. In this letter, more appropriate priors are proposed in the language of Hierarchical Bayesian Modeling, where the properties of the ensemble of pulsars are jointly described with the properties of the individual components of the ensemble. Results by Pulsar Timing Array projects should be re-evaluated using Hierarchical Models.