Optimising transient discovery with Swift-XRT
The Living Swift-XRT Point Source Catalogue (LSXPS) enables near real-time searches for X-ray transients. Many detected candidates are faint, often near the XRT detection limit, and are classed as "low significance," as it is often unclear whether their apparent brightening reflects a genuine transient or a statistical fluctuation. Some of these sources are affected by Eddington bias, a statistical effect that inflates measured fluxes near the detection threshold. We present a simulation-based Bayesian framework that corrects for this bias and provides more accurate probabilities for each source being truly transient, i.e. that its true intensity exceeds the historical 3$\sigma$ upper limit. Applied to LSXPS data, this method yields more reliable classifications, recovering over 500 transients above this threshold -- more than an eight-fold increase over the original confirmed sample. Using extensive simulations based on real Swift-XRT images, we validate the robustness of this approach, showing that it remains stable across varying exposure times and background conditions. These results demonstrate that the LSXPS transient probabilities, corrected for Eddington bias, provide a reliable and internally consistent framework for real-time X-ray transient identification.