Gauss.st.F: Simulate a spatio-temporal Gaussian random field on a regular...

In SepTest: Tests for First-Order Separability in Spatio-Temporal Point Processes

Simulate a spatio-temporal Gaussian random field on a regular grid

Description

Simulates a space-time Gaussian random field on a regular (x,y,t) grid. The field is returned as a 3D array and can be used as a latent field for log-Gaussian Cox process (LGCP) simulation.

Usage

Gauss.st.F(
  xlim = c(0, 1),
  ylim = c(0, 1),
  tlim = c(0, 1),
  par1 = c(1, 0.05),
  par2 = c(1, 0.06),
  sigmas = c(0.5, 0.5, 1),
  grid = c(15L, 15L, 10L)
)

Arguments

xlim, ylim, tlim	Numeric vectors of length 2 giving the ranges for the spatial and temporal axes. Defaults are c(0,1) for each.
par1	Numeric vector of length 2 giving the temporal covariance parameters c(variance, scale) for an exponential covariance var * exp(-d/scale).
par2	Numeric vector of length 2 giving the spatial covariance parameters c(variance, scale) for an exponential covariance var * exp(-d/scale).
sigmas	Numeric vector of length 3 specifying the weights (\sigma_1,\sigma_2,\sigma_3) for combining the spatial, temporal, and spatio-temporal components of the field.
grid	Integer vector of length 3 giving the number of grid points in the x, y, and t directions.

Details

The simulated field is a weighted sum of three independent Gaussian components:

Z(x,y,t) = \sigma_1 Z_s(x,y) + \sigma_2 Z_t(t) + \sigma_3 Z_{st}(x,y,t),

where Z_s is a purely spatial field, Z_t is a purely temporal field, and Z_{st} is a spatio-temporal field with separable exponential covariance in space and time.

The function uses mvrnorm for multivariate normal simulation and rdist to compute pairwise distances for covariance matrix construction.

Spatial and temporal covariances are exponential. The spatio-temporal component uses a separable covariance C_{st}((u,t),(u',t')) = C_s(u,u') C_t(t,t'). Simulation is performed via Cholesky factors without constructing the full (nx*ny*nt) \times (nx*ny*nt) covariance matrix.

Value

A list with components:

Z

Numeric array of dimension c(nx, ny, nt) containing simulated field values.

xcoord

Numeric vector of length nx with x-grid coordinates.

ycoord

Numeric vector of length ny with y-grid coordinates.

tcoord

Numeric vector of length nt with time-grid coordinates.

Author(s)

Mohammad Ghorbani [e-mail]
Nafiseh Vafaei [e-mail]

References

Ghorbani M., Vafaei N., Dvořák J., Myllymäki M. (2021). Testing the first-order separability hypothesis for spatio-temporal point patterns. Computational Statistics and Data Analysis, 161, 107245.

See Also

mvrnorm, rdist

Examples

 if (requireNamespace("MASS", quietly = TRUE) && requireNamespace("fields", quietly = TRUE)) {
  set.seed(1)
  field <- Gauss.st.F(
    xlim = c(0, 1), ylim = c(0, 1), tlim = c(0, 1),
    par1 = c(1, 0.05), par2 = c(1, 0.06),
    sigmas = c(0.5, 0.5, 1),
    grid = c(15, 15, 10)
  )
# Inspect dimensions and visualize one time slice
dim(field$Z)
image(field$xcoord, field$ycoord, field$Z[, , 1],
      main = "Gaussian Random Field (t = 1)",
      col = RColorBrewer::brewer.pal(11, "Spectral"))
  }

SepTest documentation built on Feb. 3, 2026, 5:07 p.m.