A sequential point process model and Bayesian inference for spatial point patterns with linear structures

We introduce a flexible spatial point process model for spatial point patterns exhibiting linear structures, without incorporating a latent line process. The model is given by an underlying sequential point process model, i.e. each new point is generated given the previous points. Under this model the points can be of one of three types: a ‘background point’, an ‘independent cluster point’, or a ‘dependent cluster point’. The background and independent cluster points are thought to exhibit ‘complete spatial randomness’, while the conditional distribution of a dependent cluster point given the previous points is such that
the dependent cluster point is likely to occur closely to a previous cluster point. We demonstrate the flexibility of the model for producing point patterns with linear structures, and propose to use the model as the likelihood in a Bayesian setting when analyzing a spatial point pattern exhibiting linear structures but where the exact mechanism responsible for the formations of lines is unknown.
We illustrate this methodology by analyzing two spatial point pattern data sets (locations of bronze age graves in Denmark and locations of mountain tops in Spain) without knowing which points are background points, independent cluster points, and dependent cluster points.