bw.scott {spatstat} | R Documentation |
Use Scott's rule of thumb to determine the smoothing bandwidth for the kernel estimation of point process intensity.
bw.scott(X, isotropic=FALSE, d=NULL) bw.scott.iso(X)
X |
A point pattern (object of class |
isotropic |
Logical value indicating whether to compute a single
bandwidth for an isotropic Gaussian kernel ( |
d |
Advanced use only. An integer value that should be used in Scott's formula instead of the true number of spatial dimensions. |
These functions select a bandwidth sigma
for the kernel estimator of point process intensity
computed by density.ppp
or density.lpp
or other appropriate functions.
They can be applied to a point pattern
belonging to any class "ppp"
, "lpp"
, "pp3"
or "ppx"
.
The bandwidth σ is computed by the rule of thumb of Scott (1992, page 152, equation 6.42). The bandwidth is proportional to n^(-1/(d+4)) where n is the number of points and d is the number of spatial dimensions.
This rule is very fast to compute. It typically produces a larger bandwidth
than bw.diggle
. It is useful for estimating
gradual trend.
If isotropic=FALSE
(the default), bw.scott
provides a
separate bandwidth for each coordinate axis, and the result of the
function is a vector, of length equal to the number of coordinates.
If isotropic=TRUE
, a single bandwidth value is computed
and the result is a single numeric value.
bw.scott.iso(X)
is equivalent to
bw.scott(X, isotropic=TRUE)
.
The default value of d is as follows:
class | dimension |
"ppp" | 2 |
"lpp" | 1 |
"pp3" | 3 |
"ppx" | number of spatial coordinates |
The use of d=1
for point patterns on a linear network
(class "lpp"
) was proposed by McSwiggan et al (2016)
and Rakshit et al (2019).
A numerical value giving the selected bandwidth, or a numerical vector giving the selected bandwidths for each coordinate.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
Scott, D.W. (1992) Multivariate Density Estimation. Theory, Practice and Visualization. New York: Wiley.
McSwiggan, G., Baddeley, A. and Nair, G. (2016) Kernel density estimation on a linear network. Scandinavian Journal of Statistics 44 (2) 324–345.
Rakshit, S., Davies, T., Moradi, M., McSwiggan, G., Nair, G., Mateu, J. and Baddeley, A. (2019) Fast kernel smoothing of point patterns on a large network using 2D convolution. International Statistical Review 87 (3) 531–556. DOI: 10.1111/insr.12327.
density.ppp
,
bw.diggle
,
bw.ppl
,
bw.CvL
,
bw.frac
.
hickory <- split(lansing)[["hickory"]] b <- bw.scott(hickory) b plot(density(hickory, b)) bw.scott.iso(hickory) bw.scott(chicago) bw.scott(osteo$pts[[1]])