Correcting for Evidence Uncertainty in the Templated Background Search for the Stochastic Gravitational-Wave Background

Abstract

We report a new source of systematic bias in the Bayesian Templated Background Search (TBS) for the astrophysical stochastic gravitational-wave background. This bias arises from the statistical uncertainty in nested sampling evidence estimates at the segment level and persists even when the likelihood model accurately characterizes the data. Using an analytically tractable model and a frequency-domain mock data analysis with an astrophysically motivated binary black hole population, we show that this uncertainty coherently inflates the inferred duty cycle by up to an order of magnitude when millions of segments are accumulated. We propose a simple and efficient correction and demonstrate its effectiveness across all tested configurations. We also find that a search prior restricted to high optimal signal-to-noise ratio (SNR) misattributes intermediate-strength signals, while extending the prior to support weaker signals amplifies the evidence uncertainty. Both the correction and careful search prior design are essential for robust inference as TBS analyses scale to upcoming observing runs.