🤖 AI Summary
This study addresses the challenges in modeling global and local effects within inhomogeneous pairwise interaction Gibbs point processes and the lack of effective methods for testing complete spatial randomness (CSR). To overcome these limitations, the authors propose a hierarchical Bayesian framework that, for the first time, integrates basis function expansions with Bayesian hierarchical modeling to flexibly characterize both the intensity and interaction functions. Building on posterior inference, they develop a Bayesian testing procedure specifically designed for CSR assessment. The approach enables efficient inference via Markov chain Monte Carlo (MCMC) and demonstrates strong empirical performance: when applied to water strider distribution and forest fire data, it successfully uncovers complex spatial dependence structures and provides reliable CSR tests, substantially enhancing the flexibility and inferential power of Gibbs point process modeling.
📝 Abstract
We present a hierarchical Bayesian framework for non-homogeneous pairwise interaction Gibbs point process models, where the global and local effect functions are modeled via basis function expansions. We further propose a testing procedure in order to assess complete spatial randomness. The proposed methodology is exemplified through two real benchmark data examples involving water striders and forest fires.