| rPSNCP {spatstat.core} | R Documentation |
Generate a random multitype point pattern, a realisation of the product shot-noise Cox process.
rPSNCP(lambda=rep(100, 4), kappa=rep(25, 4), omega=rep(0.03, 4),
alpha=matrix(runif(16, -1, 3), nrow=4, ncol=4),
kernels=NULL, nu.ker=NULL, win=owin(), nsim=1, drop=TRUE,
...,
cnames=NULL, epsth=0.001)
lambda |
List of intensities of component processes. Either a
numberic vector determining the constant (homogeneous) intensities
or a list of pixel images (objects of class |
kappa |
Numeric vector of intensities of the Poisson process of cluster centres
for component processes. Must have the same size as |
omega |
Numeric vector of bandwidths of cluster dispersal kernels
for component processes. Must have the same size as |
alpha |
Matrix of interaction parameters. Square numeric matrix with the same
number of rows and columns as the length of |
kernels |
Vector of character string determining the cluster dispersal kernels
of component processes. Impleneted kernels are Gaussian
kernel ( |
nu.ker |
Numeric vector of bandwidths of shape parameters for Varaince-Gamma kernels. |
win |
Window in which to simulate the pattern.
An object of class |
nsim |
Number of simulated realisations to be generated. |
cnames |
Optional vector of character strings giving the names of the component processes. |
... |
Optional arguments passed to |
epsth |
Numerical threshold to determine the maximum interaction range for cluster kernels. |
drop |
Logical. If |
This function generates a realisation of a product shot-noise Cox process (PSNCP). This is a multitype (multivariate) Cox point process in which each element of the multivariate random intensity Λ(u) of the process is obtained by
Lambda[i](u) = lambda[i](u) S[i](u) prod[j != i] E[ji](u)
where λ[i](u) is the intensity of component i of the process,
S[i](u) = 1 / (kappa[i]) sum[v in Phi[i]] k[i](u - v)
is the shot-noise random feild for component i and
E[ji](u) = exp(-κ[j] α[ji] / k[j](0)) prod[v in Phi[j]] (1 + alpha[ji] k[j](u-v) / k[j](0))
is a product field controlling impulses from the parent Poisson process Φ[j] with constant intensity κ[j] of component process j on Λ[i](u). Here k[i](u) is an isotropic kernel (probability density) function on R^2 with bandwidth ω[i] and shape parameter ν[i], and α[j,i] > -1 is the interaction parameter.
A point pattern (an object of class "ppp") if nsim=1, or a
list of point patterns if nsim > 1. Each point pattern is
multitype (it carries a vector of marks which is a factor).
Abdollah Jalilian. Modified by Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
Jalilian, A., Guan, Y., Mateu, J. and Waagepetersen, R. (2015) Multivariate product-shot-noise Cox point process models. Biometrics 71(4), 1022–1033.
rmpoispp,
rThomas,
rVarGamma,
rCauchy,
rNeymanScott
online <- interactive()
# Example 1: homogeneous components
lambda <- c(250, 300, 180, 400)
kappa <- c(30, 25, 20, 25)
omega <- c(0.02, 0.025, 0.03, 0.02)
alpha <- matrix(runif(16, -1, 1), nrow=4, ncol=4)
if(!online) lambda <- lambda/10
X <- rPSNCP(lambda, kappa, omega, alpha)
if(online) {
plot(X)
plot(split(X))
}
#Example 2: inhomogeneous components
z1 <- scaletointerval.im(bei.extra$elev, from=0, to=1)
z2 <- scaletointerval.im(bei.extra$grad, from=0, to=1)
if(!online) {
## reduce resolution to reduce check time
z1 <- as.im(z1, dimyx=c(40,80))
z2 <- as.im(z2, dimyx=c(40,80))
}
lambda <- list(
exp(-8 + 1.5 * z1 + 0.5 * z2),
exp(-7.25 + 1 * z1 - 1.5 * z2),
exp(-6 - 1.5 * z1 + 0.5 * z2),
exp(-7.5 + 2 * z1 - 3 * z2))
kappa <- c(35, 30, 20, 25) / (1000 * 500)
omega <- c(15, 35, 40, 25)
alpha <- matrix(runif(16, -1, 1), nrow=4, ncol=4)
if(!online) lambda <- lapply(lambda, "/", e2=10)
sapply(lambda, integral)
X <- rPSNCP(lambda, kappa, omega, alpha, win = bei$window, dimyx=dim(z1))
if(online) {
plot(X)
plot(split(X), cex=0.5)
}