Statistical significance of spatial and temporal clustering

Establish the statistical significance of the apparent spatial and temporal clustering of the eleven transients in the APPLAUSE Doppel-Reflektor plate dataset, explicitly accounting for the dataset's non-uniform sky and time sampling.

Background

The detected events are concentrated in two small regions on the sky and within a restricted time window (1949–1953), despite broader coverage in both sky position and time. This suggests potential clustering, but the dataset's non-uniform sampling complicates inference.

Quantifying whether the observed clustering deviates from expectations under the survey's selection function is necessary to evaluate hypotheses about common origins or causal relationships among events.