A global p-astro for gravitational-waves: consistently combining information from multiple search pipelines

Recent LVK analyses have used p-astro to characterize the significance of gravitational-wave candidates. Unlike false alarm rates which only capture the statistics of the instrumental noise triggers, p-astro incorporates the rate at which triggers are generated by both real signals and instrumental noise in estimating the probability that a candidate is real. The LVK Collaboration employs multiple search pipelines, each of which independently calculates p-astro values. However, the comparison of these numbers across pipelines is complicated by the fact that they are tuned in different ways and make different population assumptions. Multiple p-astro values also make the interpretation of marginal candidates more ambiguous. We develop a statistical formalism to calculate a joint p-astro for a gravitational-wave candidate, consistently accounting for triggers from all pipelines. We demonstrate the properties of this method using a toy model and by application to the publicly available list of gravitational-wave candidates from the O3a run.