densityVoronoi.stlpp: Intensity estimate of spatio-temporal point pattern using...

In stlnpp: Spatio-Temporal Analysis of Point Patterns on Linear Networks

Intensity estimate of spatio-temporal point pattern using Voronoi-Dirichlet tessellation

Description

This function performs adaptive intensity estimation for spatio-temporal point patterns on linear networks using Voronoi-Dirichlet tessellation.

Usage

## S3 method for class 'stlpp'
densityVoronoi(X, f = 1, nrep = 1, separable=FALSE, at=c("points","pixels"), dimt=128,...)

Arguments

X	an object of class stlpp
f	fraction (between 0 and 1 inclusive) of the data points that will be used to build a tessellation for the intensity estimate
nrep	number of independent repetitions of the randomised procedure
separable	logical. If FALSE, it then calculates a pseudo-separable estimate
at	string specifying whether to compute the intensity values at a grid of pixel locations and time (at="pixels") or only at the points of x (at="points"). default is to estimate the intensity at pixels
dimt	the number of equally spaced points at which the temporal density is to be estimated. see density
...	arguments passed to densityVoronoi.lpp

Details

This function computes intensity estimates for spatio-temporal point patterns on linear networks using Voronoi-Dirichlet tessellation. Both first-order separability and pseudo-separability assumptions are accommodated in the function.

If separable=TRUE, the estimated intensities will be a product of the estimated intensities on the network and those on time. Estimated intensity of the spatial component will be obtained using densityVoronoi.lpp, whereas estimated intensities of the temporal component will be obtained via densityVoronoi.tpp. If f=1, the function calculates the estimations based on the original Voronoi intensity estimator.

If separable=FALSE, the estimated intensities will be calculated based on a sub-sampling technique explained in Mateu et al. (2019). nrep sub-samples will be obtained from X based on a given retention probability f, the function densityVoronoi.stlpp, considering separable=TRUE and f=1, will be applied to each obtained sub-sample, and finally, the estimated intensities will be the sum of all obtained estimated intensities from all sub-samples divided by the (f * nrep).

Value

If at="points": a vector of intensity values at the data points of X.

If at="pixels": a list of images on a linear network. Each image represents an estimated spatio-temporal intensity at a fixed time.

Author(s)

Mehdi Moradi <[e-mail]> and Ottmar Cronie

References

Mateu, J., Moradi, M., & Cronie, O. (2019). Spatio-temporal point patterns on linear networks: Pseudo-separable intensity estimation. Spatial Statistics, 100400.

See Also

densityVoronoi.lpp, density.stlpp

Examples

 
X <- rpoistlpp(.2,a=0,b=5,L=easynet)
densityVoronoi(X)

stlnpp documentation built on May 29, 2024, 5 a.m.