Macroseismic intensity probability in the context of Bayesian Natural Neighbours

The spatial distribution of seismic effects, quantified in terms of macroseismic intensity, forms the basis for a wide range of seismic analyses and hazard assessments. Voronoi tessellation provides an effective framework for representing discrete macroseismic observations in two dimensions. Building on this premise, we present a probabilistic method for assessing the reliability of intensity estimates at unobserved locations. The proposed approach reinterprets Sibson’s Natural Neighbour weights within a Bayesian framework, treating them as prior probabilities over discrete intensity variables. The method is applied to site-specific hazard assessment in Campotosto (Central Italy) and to the Lunigiana earthquake of 11 April 1837 Mw 5.9, with comparisons to intensity prediction equations (IPEs). The results demonstrate that the method captures spatial variability consistent with macroseismic observations, providing a site-dependent measure of agreement between empirical data and model predictions. Furthermore, the probabilistic formulation enables estimating the spatial uncertainty inherent in Sibson interpolation. The Bayesian Natural Neighbours approach improves intensity mapping under data-scarce conditions and offers a flexible framework for probabilistic inference, consistency analysis, and integration with existing hazard models.