# intensity.ppm

##### Intensity of Fitted Point Process Model

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.

##### 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`

.

##### Value

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

##### 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

##### 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)
# }
```

*Documentation reproduced from package spatstat, version 1.49-0, License: GPL (>= 2)*