Model Dependence of Bayesian Gravitational-Wave Background Statistics for Pulsar Timing Arrays

TL;DR

This study demonstrates that the choice of red noise models and priors in Bayesian analyses significantly influences gravitational-wave background estimates from pulsar timing arrays, affecting both upper limits and amplitude measurements.

Contribution

It reveals the impact of model and prior choices on GWB statistics and introduces a dropout model to improve estimation accuracy.

Findings

Red noise model details greatly affect GWB upper limits and estimates.

Uniform priors on red noise amplitude often underestimate the true GWB amplitude.

Dropout models enhance the robustness of GWB parameter estimation.

Abstract

Pulsar timing array (PTA) searches for a gravitational-wave background (GWB) typically include time-correlated "red" noise models intrinsic to each pulsar. Using a simple simulated PTA dataset with an injected GWB signal we show that the details of the red noise models used, including the choice of amplitude priors and even which pulsars have red noise, have a striking impact on the GWB statistics, including both upper limits and estimates of the GWB amplitude. We find that the standard use of uniform priors on the red noise amplitude leads to 95% upper limits, as calculated from one-sided Bayesian credible intervals, that are less than the injected GWB amplitude 50% of the time. In addition, amplitude estimates of the GWB are systematically lower than the injected value by 10-40%, depending on which models and priors are chosen for the intrinsic red noise. We tally the effects of model and prior choice and demonstrate how a "dropout" model, which allows flexible use of red noise models in a Bayesian approach, can improve GWB estimates throughout.