IAS-Seminar "Statistical Assessment of 2-Dimensional Spatial Randomness in Applied Settings"

Referent:

Prof. Gary B. Hughes, California Polytechnic State University, San Luis Obispo, CA, USA

Abstract:

Consider a set of discrete points which are contained in a continuous and contiguous 2-dimensional spatial domain. The spatial point pattern might be described as random if the arrangement lacks regularity. A common definition of spatial randomness requires two properties: (1) the point density (the mean number of points per unit area) is constant within any sub-region of the domain; (2) the position of any point is independent of the location of any other point. The definition is used as a basis to assess the randomness of a given point pattern, and several unique approaches have been developed. The definition suggests directly that any equal-areas partition of the domain should produce point counts that are Poisson distributed. Any convenient partitioning can be employed, such as quadrats, and a Poisson goodness-of-fit test can be performed with the quadrat counts. Formal methods based on the distribution of nearest-neighbor distances are also useful.

It has been shown that nearest-neighbor distances in a spatially random pattern follow a Rayleigh distribution, creating another opportunity for a goodness-offit test. A third unique approach, the Clark-Evans test, exploits the central limit theorem to generate a nearest-neighbor statistic that is normally distributed. The Clark-Evans statistic is able to distinguish between patterns that are more clustered than random, and patterns that are more uniform than random. Practical utility of the Clark-Evans test is demonstrated in the context of grading image focal planes for the presence of visual anomalies. It is also likely that the method has some benefit for validation of pedestrian dynamics models, such as by comparing the Clark-Evans statistic for simulated and measured pedestrian locations in a snap-shot, or perhaps how the statistic evolves through time.

Ansprechpartner: Dr. Mohcine Chraibi, IAS-7