The solutions to many mathematical questions, both pure and applied, rely on the
ability of the investigator to uncover a pattern. In basic terms, Point Pattern Analysis is an
investigation focused on finding patterns in data comprised of points in a spatial region.
One common application of Point Pattern Analysis is epidemiology. The medical
community is often interested in the spread of infectious disease such as: SARS, chicken
pox, and West Nile virus among others. It is possible to identify pattern to the spread of
infection then this might lead to an understanding of how the spread of an illness is
related to social behavior, environmental factors, genetic susceptibility, or many other
health care factors.
In general, a spatial data set takes the form: X=
. However, it is
possible for the data to contain spatial location plus additional information. For example,
earthquake data typically gives the location of earthquakes along a fault line and will
often have the size and the time of each earthquake. Data that contains spatial data plus
additional information is often referred to as
marked spatial data
. In our analysis, we will
be concerned with only the spatial information and we will disregard any additional
information associated with the data. Moreover, the examples we will work with are
limited to two-dimensional data.
Our interest will lie in quantifying the dispersion of objects within a confined
geographical area. We try to understand the interaction of pattern and process and use
point pattern analysis as a mechanism for detecting patterns associated as compared to
random processes. The random process that will serve for our comparison will be the
homogenous Poisson process, which will be described in more detail in section 2.
D.J Gerrard describes an investigation of a 19 .6 acre square plot in Lansing Woods,
Michigan . This data includes hickories, maples and oaks grown on a square plot. The
data for hickories is given in Cartesian coordinates, that is,
) form, where
. Also, the points are plotted on a unit square region.Our main goal of Point
Pattern Analysis is to find out whether the distribution of the hickory trees is random,
clustered or regularly dispersed. The kind of pattern involved would further our
understanding of the behavior of the hickory trees and thus can be of great use to