Modeling fixation locations using spatial point processes

Spatial Point Processes

Property (iv) is called boundedly finite. So, when we use (iv) instead of (iii), we are interested in simple, boundedly finite spatial point processes with no fixed atoms. When we use (iii), the domain A can be an arbitrary set. When we use (iv), the domain A must have some notion of boundedness. This is no problem when A is a subset of Rd for some d. We just use the usual notion of boundedness...

Point processes , spatial – temporal

Transforming spatial point processes into Poisson processes

In 1986, Merzbach and Nualart demonstrated a method of transforming a two-parameter point process into a planar Poisson process of unit rate, using random stopping sets. Merzbach and Nualart's theorem applies only to a special class of point processes, since it requires two restrictive conditions: the (F4) condition of conditional independence and the convexity of the 1-compensator. The (F4) co...

Thinning spatial point processes into Poisson processes

This paper describes methods for randomly thinning certain classes of spatial point processes. In the case of a Markov point process, the proposed method involves a dependent thinning of a spatial birth-and-death process, where clans of ancestors associated with the original points are identified, and where one simulates backwards and forwards in order to obtain the thinned process. In the case...

Filters for Spatial Point Processes

We study the general problem of estimating a ‘hidden’ point process X given the realisation of an ‘observed’ point process Y (possibly defined in different spaces) with known joint distribution. We characterise the posterior distribution of X under marginal Poisson and Gauss-Poisson prior and when the transformation from X to Y includes thinning, displacement and augmentation with extra points....