R: Predicted Variance of the Number of Points

varcount {spatstat} | R Documentation

## Predicted Variance of the Number of Points

### Description

Given a fitted point process model, calculate the predicted variance of the number of points in a nominated set `B`.

### Usage

    varcount(model, B, ..., dimyx = NULL)

### Arguments

`model` | A fitted point process model (object of class `"ppm"`, `"kppm"` or `"dppm"`).
`B` | A window (object of class `"owin"` specifying the region in which the points are counted. Alternatively a pixel image (object of class `"im"`) or a function of spatial coordinates specifying a numerical weight for each random point.
`...` | Additional arguments passed to `B` when it is a function.
`dimyx` | Spatial resolution for the calculations. Argument passed to `as.mask`.

### Details

This command calculates the variance of the number of points falling in a specified window `B` according to the `model`. It can also calculate the variance of a sum of weights attached to each random point.

The `model` should be a fitted point process model (object of class `"ppm"`, `"kppm"` or `"dppm"`).

- If `B` is a window, this command calculates the variance of the number of points falling in `B`, according to the fitted `model`.

  If the `model` depends on spatial covariates other than the Cartesian coordinates, then `B` should be a subset of the domain in which these covariates are defined.

- If `B` is a pixel image, this command calculates the variance of T = sum[i] B(x[i]), the sum of the values of `B` over all random points falling in the domain of the image.

  If the `model` depends on spatial covariates other than the Cartesian coordinates, then the domain of the pixel image, `as.owin(B)`, should be a subset of the domain in which these covariates are defined.

- If `B` is a `function(x,y)` or `function(x,y,...)` this command calculates the variance of T = sum[i] B(x[i]), the sum of the values of `B` over all random points falling inside the window `W=as.owin(model)`, the window in which the original data were observed.

The variance calculation involves the intensity and the pair correlation function of the model. The calculation is exact (up to discretisation error) for models of class `"kppm"` and `"dppm"`, and for Poisson point process models of class `"ppm"`. For Gibbs point process models of class `"ppm"` the calculation depends on the Poisson-saddlepoint approximations to the intensity and pair correlation function, which are rough approximations. The approximation is not yet implemented for some Gibbs models.

### Value

A single number.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk

### See Also

`predict.ppm`, `predict.kppm`, `predict.dppm`

### Examples

       fitT <- kppm(redwood ~ 1, "Thomas")
       B <- owin(c(0, 0.5), c(-0.5, 0))
       varcount(fitT, B)

       fitS <- ppm(swedishpines ~ 1, Strauss(9))
       BS <- square(50)
       varcount(fitS, BS)

[Package spatstat version 1.63-3 Index]