sample.lgcp: Sample from an inhomogeneous Poisson process

In inlabru: Bayesian Latent Gaussian Modelling using INLA and Extensions

Sample from an inhomogeneous Poisson process

Description

This function provides point samples from one- and two-dimensional inhomogeneous Poisson processes. The log intensity has to be provided via its values at the nodes of an fm_mesh_1d or fm_mesh_2d object. In between mesh nodes the log intensity is assumed to be linear.

Usage

sample.lgcp(
  mesh,
  loglambda,
  strategy = NULL,
  R = NULL,
  samplers = NULL,
  ignore.CRS = FALSE
)

Arguments

mesh	An fmesher::fm_mesh_1d or fmesher::fm_mesh_2d object
loglambda	vector or matrix; A vector of log intensities at the mesh vertices (for higher order basis functions, e.g. for fm_mesh_1d meshes, loglambda should be given as mesh$m basis function weights rather than the values at the mesh$n vertices) A single scalar is expanded to a vector of the appropriate length. If a matrix is supplied, one process sample for each column is produced.
strategy	Only relevant for 2D meshes. One of 'triangulated', 'rectangle', 'sliced-spherical', 'spherical'. The 'rectangle' method is only valid for CRS-less flat 2D meshes. If NULL or 'auto', the the likely fastest method is chosen; 'rectangle' for flat 2D meshes with no CRS, 'sliced-spherical' for CRS 'longlat' meshes, and 'triangulated' for all other meshes.
R	Numerical value only applicable to spherical and geographical meshes. It is interpreted as R is the equivalent Earth radius, in km, used to scale the lambda intensity. For CRS enabled meshes, the default is 6371. For CRS-less spherical meshes, the default is 1.
samplers	A SpatialPolygonsDataFrame or fm_mesh_2d object. Simulated points that fall outside these polygons are discarded.
ignore.CRS	logical; if TRUE, ignore any CRS information in the mesh. Default FALSE. This affects R and the permitted values for strategy.

Details

For 2D processes on a sphere the R parameter can be used to adjust to sphere's radius implied by the mesh. If the intensity is very high the standard strategy "spherical" can cause memory issues. Using the "sliced-spherical" strategy can help in this case.

• For crs-less meshes on R2: Lambda is interpreted in the raw coordinate system. Output has an NA CRS.

• For crs-less meshes on S2: Lambda with raw units, after scaling the mesh to radius R, if specified. Output is given on the same domain as the mesh, with an NA CRS.

• For crs meshes on R2: Lambda is interpreted as per km^2, after scaling the globe to the Earth radius 6371 km, or R, if specified. Output given in the same CRS as the mesh.

• For crs meshes on S2: Lambda is interpreted as per km^2, after scaling the globe to the Earth radius 6371 km, or R, if specified. Output given in the same CRS as the mesh.

Value

A data.frame (1D case), SpatialPoints (2D flat and 3D spherical surface cases) SpatialPointsDataFrame (2D/3D surface cases with multiple samples). For multiple samples, the data.frame output has a column 'sample' giving the index for each sample. object of point locations.

Author(s)

Daniel Simpson [e-mail] (base rectangle and spherical algorithms), Fabian E. Bachl [e-mail] (inclusion in inlabru, sliced spherical sampling), Finn Lindgren [e-mail] (extended CRS support, triangulated sampling)

Examples

# The INLA package is required
if (bru_safe_inla() &&
  bru_safe_sp() &&
  require("sp")) {
  vertices <- seq(0, 3, by = 0.1)
  mesh <- fm_mesh_1d(vertices)
  loglambda <- 5 - 0.5 * vertices
  pts <- sample.lgcp(mesh, loglambda)
  pts$y <- 0
  plot(vertices, exp(loglambda), type = "l", ylim = c(0, 150))
  points(pts, pch = "|")
}



# The INLA package is required
if (bru_safe_inla() &&
  require(ggplot2, quietly = TRUE) &&
  bru_safe_sp() &&
  require("sp") &&
  require("terra", quietly = TRUE) &&
  require("sf", quietly = TRUE)) {
  gorillas <- gorillas_sp()
  pts <- sample.lgcp(gorillas$mesh,
    loglambda = 1.5,
    samplers = gorillas$boundary
  )
  ggplot() +
    gg(gorillas$mesh) +
    gg(pts)
}

inlabru documentation built on April 3, 2025, 10:54 p.m.