A marked point process perspective in fitting spatial point process models

Abstract

This paper discusses a new perspective in fitting spatial point process models. Specifically the spatial point process of interest is treated as a marked point process where at each observed event x a stochastic process M ( x ; t ) , 0 < t < r , is defined. Each mark process M ( x ; t ) is compared with its expected value, say F ( t ; θ ) , to produce a discrepancy measure at x , where θ is a set of unknown parameters. All individual discrepancy measures are combined to define an overall measure which will then be minimized to estimate the unknown parameters. The proposed approach can be easily applied to data with sample size commonly encountered in practice. Simulations and an application to a real data example demonstrate the efficacy of the proposed approach.