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Log Gaussian Cox process (LGCP) inference using INLA

Source: R/bru.inference.R
lgcp.Rd

This function performs inference on a LGCP observed via points residing possibly multiple dimensions. These dimensions are defined via the left hand side of the formula provided via the model parameter. The left hand side determines the intensity function that is assumed to drive the LGCP. This may include effects that lead to a thinning (filtering) of the point process. By default, the log intensity is assumed to be a linear combination of the effects defined by the formula's RHS.

More sophisticated models, e.g. non-linear thinning, can be achieved by using the predictor argument. The latter requires multiple runs of INLA for improving the required approximation of the predictor. In many applications the LGCP is only observed through subsets of the dimensions the process is living in. For example, spatial point realizations may only be known in sub-areas of the modelled space. These observed subsets of the LGCP domain are called samplers and can be provided via the respective parameter. If samplers is NULL it is assumed that all of the LGCP's dimensions have been observed completely.

Usage

lgcp(
  components,
  data,
  domain = NULL,
  samplers = NULL,
  ips = NULL,
  formula = . ~ .,
  ...,
  options = list(),
  .envir = parent.frame()
)

Arguments

components

A formula-like specification of latent components. Also used to define a default linear additive predictor. See bru_component() for details.

data

Likelihood-specific data, as a data.frame or SpatialPoints[DataFrame] object.

domain, samplers, ips

Arguments used for family="cp".

domain

Named list of domain definitions.

samplers

Integration subdomain for 'cp' family.

ips

Integration points for 'cp' family. Defaults to fmesher::fm_int(domain, samplers). If explicitly given, overrides domain and samplers.

formula

a formula where the right hand side is a general R expression defines the predictor used in the model.

...

Further arguments passed on to bru_obs(). In particular, optional E, a single numeric used rescale all integration weights by a fixed factor.

options

A bru_options options object or a list of options passed on to bru_options()

.envir

The evaluation environment to use for special arguments (E, Ntrials, weights, and scale) if not found in response_data or data. Defaults to the calling environment.

Value

An bru() object

Examples

# \donttest{
if (bru_safe_inla() &&
  require(ggplot2, quietly = TRUE) &&
  require(fmesher, quietly = TRUE) &&
  require(sn, quietly = TRUE)) {
  # Load the Gorilla data
  data <- gorillas_sf

  # Plot the Gorilla nests, the mesh and the survey boundary
  ggplot() +
    geom_fm(data = data$mesh) +
    gg(data$boundary, fill = "blue", alpha = 0.2) +
    gg(data$nests, col = "red", alpha = 0.2)

  # Define SPDE prior
  matern <- INLA::inla.spde2.pcmatern(
    data$mesh,
    prior.sigma = c(0.1, 0.01),
    prior.range = c(0.1, 0.01)
  )

  # Define domain of the LGCP as well as the model components (spatial SPDE
  # effect and Intercept)
  cmp <- geometry ~ field(geometry, model = matern) + Intercept(1)

  # Fit the model (with int.strategy="eb" to make the example take less time)
  fit <- lgcp(cmp, data$nests,
    samplers = data$boundary,
    domain = list(geometry = data$mesh),
    options = list(control.inla = list(int.strategy = "eb"))
  )

  # Predict the spatial intensity surface
  lambda <- predict(
    fit,
    fm_pixels(data$mesh, mask = data$boundary),
    ~ exp(field + Intercept)
  )

  # Plot the intensity
  ggplot() +
    gg(lambda, geom = "tile") +
    geom_fm(data = data$mesh, alpha = 0, linewidth = 0.05) +
    gg(data$nests, col = "red", alpha = 0.2)
}

# }