A new thinning method of spatial point processes based on using Boolean random set models

Spatial point processes are statistical models for the analysis of point patterns. One approach to constructing new point processes is thinning an existing point process. In this paper, we introduce a new dependent thinning algorithm based on a Boolean random set, which generalizes the Stoyan thinning algorithm for interrupted point processes. The proposed algorithm generates both a thinned point process and a deleted point process. Summary statistics and limiting behavior are derived for these point processes. This paper focuses exclusively on the deleted points process and compares its performance with an existing process via the AIC criterion. The Palm likelihood method is employed for parameter estimation, and theoretical identifiability of the model parameters is established. Finally, the proposed model is applied to a real dataset, demonstrating its practical utility.