sim_lgcp_multi: Simulation of semi-parametric multivariate log Gaussian Cox...

In kristianhessellund/Multilogreg: Semi-parametric models for multivariate point pattern data

Description

Simulation of semi-parametric multivariate log Gaussian Cox processes.

Usage

sim_lgcp_multi(
  basecov,
  covariate,
  betas,
  alphas,
  xis,
  sigmas,
  phis,
  n.window,
  n.points,
  beta0s = NULL
)

Arguments

basecov	Background intensity rho_0.
covariate	Optional. A simulated covariate. The covariate must be a matrix.
betas	A matrix with covariates.
alphas	Alpha parameters. Must be a matrix, where the number of rows correspond to the number of components in the LGCP. The number of columns correspond to the number of common latent field.
xis	Correlation scale parameters for each common random field. The correlation functions for the common latent fields are exponential.
sigmas	Sigma parameters. The number of sigma parameters must correspond to the number of components in the LGCP.
phis	Correlation scale parameters for each type-specific random field. The correlation functions for the type-specific random fields are exponential.
n.window	window size.
n.points	Expected number of point for each component in the LGCP. The length of n.points must correspond to the number of components.
beta0s	Intercepts. The length of beta0s must correspond to the number of components in the LGCP.

Value

Multivariate LGCP

Author(s)

Kristian Bjørn Hessellund, Ganggang Xu, Yongtao Guan and Rasmus Waagepetersen.

References

Hessellund, K. B., Xu, G., Guan, Y. and Waagepetersen, R. (2020) Second order semi-parametric inference for multivariate log Gaussian Cox processes.

Examples

# Size of the observation window
n.x <- n.y <- 1
xx=seq(0,n.x,length=100)
yy=seq(0,n.x,length=100)

# Simulating a covariate
cov <- as.matrix(RFsimulate(RMexp(var=1,scale=0.05), x=xx, y=yy, grid=TRUE))

# Simulating the background intensity
gamma <- 0.5
background <- as.matrix(RFsimulate(RMgauss(var=1,scale=0.2), x=xx, y=yy, grid=TRUE))*gamma-gamma^2/2

#Set up parameters
beta1 <- c(0.1,0.2,0.3,0.4,0.5)
beta2 <- c(-0.1,-0.2,0,0.1,0.2)
beta2 <- as.matrix(beta2)

# Parameters in the LGCP

alpha <- matrix(c(0.5,-1,0.5,0,-1,0,0,0.5,0,0.5),nrow=5,byrow=TRUE)
xi    <- c(0.02,0.03)
sigma <- matrix(c(sqrt(0.5),sqrt(0.5),sqrt(0.5),sqrt(0.5),sqrt(0.5)),ncol=1)
phi   <- matrix(c(0.02,0.02,0.03,0.03,0.04),ncol=1)

n.window <- n.x
n.points <- c(400,400,400,400,400)

# Simulation of a multivariate LGCP
X <- sim_lgcp_multi(basecov=background,covariate=cov,betas=beta2,alphas=alpha,xi=xi,
sigma=sigma,phis=phi, n.window=n.window,n.points=n.points,beta0s=beta1)

plot(X$markedprocess)

kristianhessellund/Multilogreg documentation built on Jan. 1, 2021, 7:23 a.m.