dpoisppDetection_normal {nimbleSCR}

Poisson point process detection model

Description

Density and random generation functions of the Poisson point process for detection. The dpoisppDetection_normal distribution is a NIMBLE custom distribution which can be used to model and simulate Poisson observations (x) of a single individual in continuous space over a set of detection windows defined by their upper and lower coordinates (lowerCoords,upperCoords). The distribution assumes that an individual’s detection intensity follows an isotropic bivariate normal function centered on the individual's activity center (s) with standard deviation (sd). All coordinates (s and trapCoords) should be scaled to the habitat (scaleCoordsToHabitatGrid).

Usage

dpoisppDetection_normal(
  x,
  lowerCoords,
  upperCoords,
  s,
  sd,
  baseIntensities,
  numMaxPoints,
  numWindows,
  indicator,
  log = 0
)

rpoisppDetection_normal(
  n,
  lowerCoords,
  upperCoords,
  s,
  sd,
  baseIntensities,
  numMaxPoints,
  numWindows,
  indicator
)

Arguments

x

Array containing the total number of detections (x[1,1]), the x- and y-coordinates (x[2:(x[1,1]+1),1:2]), and the corresponding detection window indices (x[2:(x[1,1]+1),3]) for a set of spatial points (detection locations).

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.

s

Vector of x- and y-coordinates of the isotropic multivariate normal distribution mean (the AC location).

sd

Standard deviation of the isotropic multivariate normal distribution.

baseIntensities

Vector of baseline detection intensities for all detection windows.

numMaxPoints

Maximum number of points. This value (non-negative integer) is only used when simulating detections to constrain the maximum number of detections.

numWindows

Number of detection windows. This value (positive integer) is used to truncate lowerCoords and upperCoords so that extra rows beyond numWindows are ignored.

indicator

Binary argument specifying whether the individual is available for detection (indicator = 1) or not (indicator = 0).

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

dpoisppDetection_normal gives the (log) probability density of the observation matrix x. rpoisppDetection_normal 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

coordsHabitatGridCenter <- matrix(c(0.5, 3.5,
                                    1.5, 3.5,
                                    2.5, 3.5,
                                    3.5, 3.5,
                                    0.5, 2.5,
                                    1.5, 2.5,
                                    2.5, 2.5,
                                    3.5, 2.5,
                                    0.5, 1.5,
                                    1.5, 1.5,
                                    2.5, 1.5,
                                    3.5, 1.5,
                                    0.5, 0.5,
                                    1.5, 0.5,
                                    2.5, 0.5,
                                    3.5, 0.5), ncol = 2,byrow = TRUE)
colnames(coordsHabitatGridCenter) <- c("x","y")
# Create observation windows
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)
colnames(lowerCoords) <- colnames(upperCoords) <- c("x","y")

# Rescale coordinates
ScaledLowerCoords <- scaleCoordsToHabitatGrid(coordsData =  lowerCoords,
                                              coordsHabitatGridCenter = coordsHabitatGridCenter)
ScaledUpperCoords <- scaleCoordsToHabitatGrid(coordsData =  upperCoords,
                                              coordsHabitatGridCenter = coordsHabitatGridCenter)
ScaledUpperCoords$coordsDataScaled[,2] <- ScaledUpperCoords$coordsDataScaled[,2] + 1.5
ScaledLowerCoords$coordsDataScaled[,2] <- ScaledLowerCoords$coordsDataScaled[,2] - 1.5



# Detection locations
x <- matrix(c(1.5, 2, 1.1, 1.5,0.6, 2.1, 0.5, 2, 1, 1.5), nrow = 5, byrow = TRUE)

# get the window indeces on the third dimension of x

windowIndexes <- 0
for(i in 1:nrow(x)){
  windowIndexes[i] <- getWindowIndex(curCoords = x[i,],
                                     lowerCoords = ScaledLowerCoords$coordsDataScaled,
                                     upperCoords = ScaledUpperCoords$coordsDataScaled)
}
x <- cbind(x, windowIndexes)
# get the total number of detections on x[1,1]
x <- rbind(c(length(windowIndexes),0,0) ,x )


s <- c(1, 1)
sd <- 0.1
baseIntensities <- c(1:4)
windowIndices <- c(1, 2, 2, 3, 4)
numPoints <- 5
numWindows <- 4
indicator <- 1
dpoisppDetection_normal(x, lowerCoords, upperCoords, s, sd, baseIntensities,
                        numMaxPoints = dim(x)[1] , numWindows, indicator, log = TRUE)