Analysing spatial point patterns in R - CSIRO

14 Statistical formulation
Example 13 A herd of deer is photographed from the air at noon each day for 10 days. Each
photograph is processed to produce a point pattern of individual deer locations on a map.
Each day produces a point pattern that could be analysed as a realisation of a point process.
However, the observations on successive days are dependent (e.g. constant herd size, systematic
foraging behaviour). Assuming individual deer cannot be identified from day to day, this is
effectively a ‘repeated measures’ dataset where each response is a point pattern. Methods for
this problem are in their infancy.
Example 14 In a designed controlled experiment, silicon wafers are produced under various
conditions. Each wafer is inspected for defects in the crystal surface, and the locations of all
defects are recorded as a point pattern.
This is a designed experiment in which the response is a point pattern. Methods for this
problem are in their infancy. There are some methods for replicated spatial point patterns
[15, 19, 36, 37, 42] that apply when each experimental group contains several point patterns.
Example 15 The points are not the original data, but were obtained after processing the data.
For example,
the original dataset is a pattern of small blobs, and the points are the blob centres;
the original dataset is a collection of line segments, and the points are the endpoints,
crossing points, midpoints etc;
the original dataset is a space-filling tessellation of biological cells, and the points are the
centres of the cells.
This is a grey area. Point process methodology can be applied, and may be more powerful
or more flexible than existing methodology for the unprocessed data. However the origin of the
point pattern may lead to artefacts (for example the centres of biological cells never lie very close
together, because cells have nonzero size) which must be taken into account in the analysis.
For more discussion about these topics, see [3].
2.3 Assumptions about the data
The “standard model” assumes that the point process X extends throughout 2-D space, but
is observed only inside a region W, the “sampling window”. Our data consist of an unordered
set
x = {x 1 ,... ,x n }, x i ∈ W, n ≥ 0
of points x i in W. The window W is fixed and known. Usually our goal is inference about
parameters of X.
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