Connectivity-Interaction point processes in experimental design: MCMC simulation and application to the Redwood seedlings dataset

Spatial point processes provide a rigorous framework for modeling random configurations of points in space. While the homogeneous Poisson point process serves as a benchmark for complete spatial randomness, more flexible models are required to capture clustering or repulsion patterns commonly observed in real applications. The Baddeley point process, belonging to the class of area- and connectivity-interaction models, is particularly well suited for attractive phenomena. In this paper, we propose a Markov Chain Monte Carlo methodology, based on the Random Walk Metropolis-Hastings algorithm, for simulating connectivity-interaction Baddeley processes and assessing their relevance for experimental design. The contributions are fourfold: (i) a study of the Markovian properties of the model; (ii) a graph-based algorithm for efficiently computing the number of connected components; (iii) an investigation of the effect of key parameters on the generated designs; and (iv) theoretical convergence results for the proposed simulation scheme. Comparative studies show that Baddeley-based designs outperform classical strategies under standard optimality criteria. Applications to numerical integration highlight their competitive accuracy and variance reduction, while analysis of the redwood seedlings dataset confirms the ability of the Baddeley process to capture clustering patterns and provide valuable insights into ecological spatial interactions.