Cox point processes

LgcpSimulate: log-Gaussian Cox process on a lattice (Cholesky field, Poisson counts, uniform positions). LgcpMoments: intensity, expected count and pair correlation. ThomasSimulate: Thomas cluster process. ThomasPcf: its pair correlation and K function. VoronoiResiduals: Voronoi residuals of a log-linear intensity. Philox draws; identical to the Python arm morie.fn.coxproc.

Usage

LgcpSimulate(window, n_grid, mu, model, seed = 1)

LgcpMoments(mu, sigma2, area, r = 0, model = NULL)

ThomasSimulate(kappa, scale, mu, window, seed = 1)

ThomasPcf(r, kappa, scale)

VoronoiResiduals(points, bbox, beta)

Arguments

window

Rectangle (xmin, xmax, ymin, ymax).

n_grid

Lattice size per side.

mu

Mean of the Gaussian field, or mean offspring number.

model

Covariance model (KrigingCovariance).

seed

Philox seed.

sigma2

Field variance.

area

Window area.

r

Distance.

kappa

Parent intensity.

scale

Offspring dispersal standard deviation.

points

Two-column matrix of points.

bbox

Box (xmin, ymin, xmax, ymax).

beta

Log-linear intensity coefficients (intercept, x, y).

Value

List.

References

Moller, J., Syversveen, A. R. and Waagepetersen, R. P. (1998). Log Gaussian Cox processes. Scandinavian Journal of Statistics 25, 451-482.

Diggle, P. J. (2013). Statistical Analysis of Spatial and Spatio-Temporal Point Patterns, 3rd edn. CRC Press.

Bray, A., Wong, K., Barr, C. D. and Schoenberg, F. P. (2014). Voronoi residual analysis of spatial point process models. Annals of Applied Statistics 8, 2247-2267.

Examples

ThomasPcf(0.1, 10, 0.05)
#> $pcf
#> [1] 2.170997
#> 
#> $K
#> [1] 0.09462798
#> 
VoronoiResiduals(rbind(c(0.25, 0.5), c(0.75, 0.5)), c(0, 0, 1, 1), c(log(2), 0, 0))$residuals
#> [1] 9.992007e-16 9.992007e-16