Estimate Intensity of Point Pattern Using Nearest Neighbour Distances
Estimates the intensity of a point pattern
using the distance from each spatial location
kth nearest data point.
## S3 method for class 'ppp': nndensity(x, k, ..., verbose = TRUE)
- A point pattern (object of class
"ppp") or some other spatial object.
- Integer. The distance to the
kth nearest data point will be computed. There is a sensible default.
- Arguments passed to
as.maskcontrolling the pixel resolution.
- Logical. If
TRUE, print the value of
kwhen it is automatically selected. If
FALSE, remain silent.
This function computes a quick estimate of the intensity of the point
process that generated the point pattern
For each spatial location $s$, let $d(s)$ be the distance from $s$
to the $k$-th nearest point in the dataset
If the data came from a homogeneous
Poisson process with intensity $\lambda$,
then $\pi d(s)^2$ would follow a
negative exponential distribution with mean
$1/\lambda$, and the maximum likelihood estimate of
$\lambda$ would be $1/(\pi d(s)^2)$.
This is the estimate computed by
apart from an edge effect correction.
This estimator of intensity is relatively fast to compute, and is spatially adaptive (so that it can handle wide variation in the intensity function). However, it implicitly assumes the points are independent, so it does not perform well if the pattern is strongly clustered or strongly inhibited.
The value of
k should be greater than 1 in order to avoid
infinite peaks in the intensity estimate around each data point.
The default value of
k is the square root of the number of
x, which seems to work well in many cases.
The window of
x is digitised using
and the values $d(s)$ are computed using
To control the pixel resolution, see
- A pixel image (object of class
"im") giving the estimated intensity of the point process at each spatial location. Pixel values are intensities (number of points per unit area).
NEED REFERENCES. TRY CRESSIE