Point Processes in Spatial Statistics
The analysis of point pattern data in a compact subset S of Rn is a major object of study within spatial statistics. Such data appear in a broad range of disciplines, amongst which are
- forestry and plant ecology (positions of trees or plants in general)
- epidemiology (home locations of infected patients)
- zoology (burrows or nests of animals)
- geography (positions of human settlements, towns or cities)
- seismology (epicenters of earthquakes)
- materials science (positions of defects in industrial materials)
- astronomy (locations of stars or galaxies)
- computational neuroscience (spikes of neurons).
The need to use point processes to model these kinds of data lies in their inherent spatial structure. Accordingly, a first question of interest is often whether the given data exhibit complete spatial randomness (i.e. are a realization of a spatial Poisson process) as opposed to exhibiting either spatial aggregation or spatial inhibition.
In contrast, many datasets considered in classical multivariate statistics consist of independently generated datapoints that may be governed by one or several covariates (typically non-spatial).
Apart from the applications in spatial statistics, point processes are one of the fundamental objects in stochastic geometry. Research has also focussed extensively on various models built on point processes such as Voronoi Tessellations, Random geometric graphs, Boolean model etc.
Read more about this topic: Point Process
Famous quotes containing the words point, processes and/or statistics:
“Competition has been shown to be useful up to a certain point and no further, but cooperation, which is the thing we must strive for today, begins where competition leaves off.”
—Franklin D. Roosevelt (1882–1945)
“The higher processes are all processes of simplification. The novelist must learn to write, and then he must unlearn it; just as the modern painter learns to draw, and then learns when utterly to disregard his accomplishment, when to subordinate it to a higher and truer effect.”
—Willa Cather (1873–1947)
“and Olaf, too
preponderatingly because
unless statistics lie he was
more brave than me: more blond than you.”
—E.E. (Edward Estlin)