Pulsar Timing Arrays require hierarchical models

TL;DR

This paper advocates for the use of hierarchical Bayesian models in Pulsar Timing Array analyses to better account for pulsar noise properties, which can bias gravitational wave background estimates.

Contribution

It introduces hierarchical Bayesian modeling as a more suitable approach for ensemble pulsar data, replacing uninformative priors with more appropriate ones.

Findings

Hierarchical models improve parameter estimation accuracy.

Re-evaluation of PTA results with hierarchical models is recommended.

Hierarchical priors better represent pulsar noise properties.

Abstract

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.