spatstat (version 1.64-1)

intensity.ppm: Intensity of Fitted Point Process Model

Description

Computes the intensity of a fitted point process model.

Usage

# S3 method for ppm
intensity(X, …)

Arguments

X

A fitted point process model (object of class "ppm").

…

Arguments passed to predict.ppm in some cases. See Details.

Value

A numeric value (if the model is stationary) or a pixel image.

Details

This is a method for the generic function intensity for fitted point process models (class "ppm").

The intensity of a point process model is the expected number of random points per unit area.

If X is a Poisson point process model, the intensity of the process is computed exactly. The result is a numerical value if X is a stationary Poisson point process, and a pixel image if X is non-stationary. (In the latter case, the resolution of the pixel image is controlled by the arguments … which are passed to predict.ppm.)

If X is another Gibbs point process model, the intensity is computed approximately using the Poisson-saddlepoint approximation (Baddeley and Nair, 2012a, 2012b, 2016; Anderssen et al, 2014). The approximation is currently available for pairwise-interaction models (Baddeley and Nair, 2012a, 2012b) and for the area-interaction model and Geyer saturation model (Baddeley and Nair, 2016).

For a non-stationary Gibbs model, the pseudostationary solution (Baddeley and Nair, 2012b; Anderssen et al, 2014) is used. The result is a pixel image, whose resolution is controlled by the arguments … which are passed to predict.ppm.

References

Anderssen, R.S., Baddeley, A., DeHoog, F.R. and Nair, G.M. (2014) Solution of an integral equation arising in spatial point process theory. Journal of Integral Equations and Applications 26 (4) 437--453.

Baddeley, A. and Nair, G. (2012a) Fast approximation of the intensity of Gibbs point processes. Electronic Journal of Statistics 6 1155--1169.

Baddeley, A. and Nair, G. (2012b) Approximating the moments of a spatial point process. Stat 1, 1, 18--30. doi: 10.1002/sta4.5

Baddeley, A. and Nair, G. (2016) Poisson-saddlepoint approximation for spatial point processes with infinite order interaction. Submitted for publication.

See Also

intensity, intensity.ppp

Examples

# NOT RUN {
  fitP <- ppm(swedishpines ~ 1)
  intensity(fitP)
  fitS <- ppm(swedishpines ~ 1, Strauss(9))
  intensity(fitS)
  fitSx <- ppm(swedishpines ~ x, Strauss(9))
  lamSx <- intensity(fitSx)
  fitG <- ppm(swedishpines ~ 1, Geyer(9, 1))
  lamG <- intensity(fitG)
  fitA <- ppm(swedishpines ~ 1, AreaInter(7))
  lamA <- intensity(fitA)
# }