A Bayesian Hierarchical Nonoverlapping Random Disc Growth Model

Abstract

A methodology is proposed to efficiently model a random set via a multistage hierarchical Bayesian model. We define a NonOverlapping Random Disk Model (NORDM), which is similar in spirit to the well-known Poisson–Boolean model. This model is formulated in a conditional setting that facilitates Bayesian sampling of important parameters in the model. This framework can accommodate any object, not just those with disk shapes, although the model can be easily extended to include any known compact convex set instead of the disc (e.g., polygons or ellipses). We further propose a growth model that is conceptually simple and allows straightforward estimation of parameters, without the need for tedious calculations of hitting or inclusion probabilities. The model is applied to severe storm cell development as obtained from weather radar.