Illustration of non-Poisson rejection. Top panel: example of event rate as a function of time in a detector with the size of Super-Kamiokande. The injected Poisson background has a rate r_bkg = 0.05 s⁻¹. Two additional spatially correlated clusters of background events (with σ_B = 2 m) and with respectively 10 and 15 events) have been injected. Finally, two signal-like bursts with the parametrisation of Eq. (14) are added, with 7 and 10 neutrinos, respectively. Bottom panel: test statistic time evolution for the RTS² method without and with the spatial penalty from Eq. (16).