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A Sequential Point Process Model and Bayesian Inference for Spatial Point Patterns with Linear Structures

Authors


Jakob Gulddahl Rasmussen, Department of Mathematical Sciences, Aalborg University, Fredrik Bajersvej 7E, DK-9220 Aalborg.
E-mail: jgr@math.aau.dk

Abstract

Abstract.  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. 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’, whereas the dependent cluster points are likely to occur close to previous cluster points. 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 analysing a spatial point pattern exhibiting linear structures. We illustrate this methodology by analysing two spatial point pattern datasets (locations of bronze age graves in Denmark and locations of mountain tops in Spain).

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