dpoisppAC {nimbleSCR}

Poisson point process for the distribution of activity centers

Description

Density and random generation functions of the Poisson point process for the distribution of activity centers. The dpoisppAC distribution is a NIMBLE custom distribution which can be used to model and simulate activity center locations (x) of multiple individual in continuous space over a set of habitat windows defined by their upper and lower coordinates (lowerCoords,upperCoords). The distribution assumes that activity centers follow a Poisson point process with intensity = exp(logIntensities). All coordinates (s and trapCoords) should be scaled to the habitat (scaleCoordsToHabitatGrid).

Usage

dpoisppAC(
  x,
  lowerCoords,
  upperCoords,
  logIntensities,
  sumIntensity,
  habitatGrid,
  numGridRows,
  numGridCols,
  numPoints,
  log = 0
)

rpoisppAC(
  n,
  lowerCoords,
  upperCoords,
  logIntensities,
  sumIntensity,
  habitatGrid,
  numGridRows,
  numGridCols,
  numPoints
)

Arguments

x

Matrix of x- and y-coordinates of a set of spatial points (AC locations) scaled to the habitat (scaleCoordsToHabitatGrid). Each row corresponds to a point.

lowerCoords, upperCoords

Matrices of lower and upper x- and y-coordinates of all detection windows scaled to the habitat (see (scaleCoordsToHabitatGrid). One row for each window. Each window should be of size 1x1.

logIntensities

Vector of log habitat intensities for all habitat windows.

sumIntensity

Sum of the habitat intensities over all windows. Provided as an argument for computational speed, instead of calculating it in the function.

habitatGrid

Matrix of habitat window indices. Cell values should correspond to the order of habitat windows in lowerCoords, upperCoords, and logIntensities. When the habitat grid only consists of a single row or column of windows, an additional row or column of dummy indices has to be added because the nimble model code requires a matrix.

numGridRows, numGridCols

Numbers of rows and columns of the habitat grid.

numPoints

Number of points in the Poisson point process. This value (non-negative integer) is used to truncate x so that extra rows beyond numPoints are ignored.

log

Logical argument, specifying whether to return the log-probability of the distribution.

n

Integer specifying the number of realisations to generate. Only n = 1 is supported.

Value

dpoisppAC gives the (log) probability density of the observation matrix x. rpoisppAC gives coordinates of a set of randomly generated spatial points.

Author(s)

Wei Zhang

References

W. Zhang, J. D. Chipperfield, J. B. Illian, P. Dupont, C. Milleret, P. de Valpine and R. Bischof. 2020. A hierarchical point process model for spatial capture-recapture data. bioRxiv. DOI 10.1101/2020.10.06.325035

Examples

lowerCoords <- matrix(c(0, 0, 1, 0, 0, 1, 1, 1), nrow = 4, byrow = TRUE)
upperCoords <- matrix(c(1, 1, 2, 1, 1, 2, 2, 2), nrow = 4, byrow = TRUE)
logIntensities <- log(c(1:4))
logSumIntensity <- sum(exp(logIntensities))
habitatGrid <- matrix(c(1:4), nrow = 2, byrow = TRUE)
numGridRows <- nrow(habitatGrid)
numGridCols <- ncol(habitatGrid)
#Simulate data
x <- rpoisppAC(1, lowerCoords, upperCoords, logIntensities, logSumIntensity, habitatGrid,
               numGridRows, numGridCols, -1)
numPoints <- nrow(x)
dpoisppAC(x, lowerCoords, upperCoords, logIntensities, logSumIntensity,
          habitatGrid, numGridRows, numGridCols, numPoints, log = TRUE)