Modelling Three-Dimensional Point Patterns

In this study, we explore the cubature scheme procedure for modelling three-dimensional point patterns through Poisson point process models, a computational realm that remains under-explored. Through simulations, we give guidelines for choosing the number of cubes to partition the observed three-dimensional region, the number of dummy points to generate, and whether to simulate them regularly or casually in space. We apply this methodology to the real observed point pattern of young stars of the Gaia Archive.