In antiphon/rcox: Simulates Cox point process, in 2D and 3D

\newcommand{\x}{\mathbf{x}}

This doc gives a short example of how to simulate shot-noise and product-noise Cox patterns in 3D.

See the "Example_1" vignette for basics.

library(rcox)

Simulation in 3D

Two examples:

set.seed(1) 
x1 <- matrix( runif( 10 * 3), ncol = 3 )
x2 <- cbind(0.5, 0.5, 0.5)
bb3 <- cbind(0:1, 0:1, 0:1) # bounding box for later

We set up the models like this:

lam1 <- lambda(x1, kernel = "gauss", sigma = 0.05, alpha = 5, type = "sum")
lam2 <- lambda(x2, kernel = "step", sigma = 0.1, alpha = c(1, 100), type = "prod")

The documentation lists the options.

Check the 3D field

One can evaluate the field at any point. Let's slice through the window with $z=0.5$ plane:

# make a slice z=0.5
ng <- seq(0, 1, l = 50)
grid3 <- as.matrix( expand.grid( ng, ng , 0.5) )
field1 <- coxintensity2matrix(lam1, bbox = bb3, at = grid3)
field2 <- coxintensity2matrix(lam2, bbox = bb3, nx = 128, at = grid3)

par(mfrow=c(1,2))
plot3 <- function(f) image(matrix(f, ncol = length(ng)), x=ng, y=ng, asp=1) 
plot3(field1)
plot3(field2)

Red means low intensity (not preferred), white means high intensity (preferred).

Simulating

The simulation uses either a thinning approach (free point count) or Metropolis-Hastings (fixed point count). The calls:

s1 <- rcox(lambda = lam1, bbox = bb3)
s2 <- rcox(lambda = lam2, bbox = bb3, n = 100)
# turn to ppp-objects
y1 <- cox2ppp(s1)
y2 <- cox2ppp(s2)

par(mfrow=c(1,2), mar=c(1,1,1,1))
plot(y1)
plot(y2)

There we have it.

EOF

antiphon/rcox documentation built on June 3, 2023, 11:07 a.m.