Quantifying Spatial Discrepancies in Gamma-Ray Bursts with Information Entropy

Assessing whether different observational selection effects and spectroscopic redshift determination methods introduce spatial biases is critical for reliable cosmological and large-scale structure studies. In this paper, we address the fundamental scientific question of whether Gamma-Ray Burst subsets obtained via rapid optical afterglow follow-ups and host galaxy observations share an identical spatial distribution. These two observational subsets are denoted as A and H, respectively, and correspond to different spectroscopic redshift determination methods acting as virtual detectors. We demonstrate a strict theoretical and statistical framework for testing this spatial invariance hypothesis using Swift Satellite data. The observed events are modeled as realizations of an inhomogeneous Poisson point process on the celestial sphere, applying a comprehensive suite of non-parametric, information-theoretic, and model selection techniques, including spatial relative risk functions, the Syrjala test, parametric bootstrap procedures, and Wasserstein/Jensen–Shannon divergences. Our results demonstrate that the spatial distributions and scale-dependent clustering properties of the two subsets are statistically indistinguishable (p = 0.41 for the Syrjala test, p = 0.76 for model selection, JSD=0.335 nats and W1=0.230 rad. for information and transport metrics, and p = 0.65 for Ripley’s L-function). Although shared large-scale structural residuals appear due to unmodeled background effects (such as the galactic plane), there is no evidence of differential spatial bias between the subsets. Consequently, these findings confirm that data from both determination methods can be reliably combined in future cosmological applications.