dbernppDetection_normal {nimbleSCR}

Bernoulli point process detection model

Description

Density and random generation functions of the Bernoulli point process for detection.

Usage

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

rbernppDetection_normal(
  n,
  lowerCoords,
  upperCoords,
  s,
  sd,
  baseIntensities,
  numWindows,
  indicator
)

Arguments

x

Vector with three elements representing the x- and y-coordinates and the id of the corresponding detection window for a single spatial point (detection location) scaled to the habitat (see (scaleCoordsToHabitatGrid).

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

VVector of x- and y-coordinates of the isotropic bivariate normal distribution mean (i.e. the AC location)..

sd

Standard deviation of the isotropic bivariate normal distribution.

baseIntensities

Vector of baseline detection intensities for all detection windows.

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.

Details

The dbernppDetection_normal distribution is a NIMBLE custom distribution which can be used to model and simulate Bernoulli 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 probability follows an isotropic multivariate normal centered on the individual's activity center (s) with standard deviation (sd).

Value

dbernppDetection_normal gives the (log) probability density of the observation vector x. rbernppDetection_normal gives coordinates of a randomly generated spatial point.

Author(s)

Wei Zhang and Cyril Milleret

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


s <- c(1, 1)
sd <- 0.1
baseIntensities <- c(1:4)
windowIndex <- 4
numPoints <- 1
numWindows <- 4
indicator <- 1
x <- c(0.5, 2)
windowIndex <- getWindowIndex(curCoords = x,
                              lowerCoords = ScaledLowerCoords$coordsDataScaled,
                              upperCoords =ScaledUpperCoords$coordsDataScaled)
x <- c(x, windowIndex)

dbernppDetection_normal(x, lowerCoords, upperCoords,
                        s, sd, baseIntensities
                        , numWindows,
                        indicator, log = TRUE)