dbernppLocalDetection_normal {nimbleSCR}

Local evaluation for a Bernoulli point process detection model

Description

Density and random generation functions of the Bernoulli point process for detection based on a bivariate normal distribution.

Usage

dbernppLocalDetection_normal(
  x,
  lowerCoords,
  upperCoords,
  s,
  sd,
  baseIntensities,
  habitatGridLocal,
  resizeFactor = 1,
  localObsWindowIndices,
  numLocalObsWindows,
  numWindows,
  indicator,
  log = 0
)

rbernppLocalDetection_normal(
  n,
  lowerCoords,
  upperCoords,
  s,
  sd,
  baseIntensities,
  habitatGridLocal,
  resizeFactor = 1,
  localObsWindowIndices,
  numLocalObsWindows,
  numWindows,
  indicator
)

Arguments

x

Vector with three elements representing the x- and y-coordinates (x[1:2]), and the corresponding id the detection window (x[3]) of 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. One row for each window. Each window should be of size 1x1 (after rescaling if necessary).

s

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

sd

Standard deviation of the bivariate normal distribution.

baseIntensities

Vector of baseline detection intensities for all detection windows.

habitatGridLocal

Matrix of rescaled habitat grid cells indices, as returned by the getLocalObjects function (object named habitatGrid).

resizeFactor

Aggregation factor used in the getLocalObjects function to reduce the number of habitat grid cells.

localObsWindowIndices

Matrix of indices of local observation windows around each local habitat grid cell (habitatGridLocal), from localIndices returned by the getLocalObjects function.

numLocalObsWindows

Vector of numbers of local observation windows around all habitat grid cells, as returned by the getLocalObjects function (object named numLocalIndices). The ith number gives the number of local (original) observation windows for the ith (rescaled) habitat window.

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 realizations 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). The local evaluation approach is implemented.

Value

The (log) probability density of the observation vector x.

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

C. Milleret, P. Dupont, C. Bonenfant, H. Brøseth, Ø. Flagstad, C. Sutherland and R. Bischof. 2019. A local evaluation of the individual state-space to scale up Bayesian spatial capture-recapture. Ecology and Evolution 9:352-363

Examples

# Create habitat grid
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(1, 1, 2, 1, 1, 2, 2, 2), nrow = 4, byrow = TRUE)
upperCoords <- matrix(c(2, 2, 3, 2, 2, 3, 3, 3), nrow = 4, byrow = TRUE)  
colnames(lowerCoords) <- colnames(upperCoords) <- c("x","y")
# Plot check
plot(coordsHabitatGridCenter[,"y"]~coordsHabitatGridCenter[,"x"],pch=16) 
points(lowerCoords[,"y"]~lowerCoords[,"x"],col="red",pch=16) 
points(upperCoords[,"y"]~upperCoords[,"x"],col="red",pch=16) 
#'
s <- c(1, 1)
sd <- 0.1
baseIntensities <- c(1:4)
windowIndex <- 4
numPoints <- 1
numWindows <- 4
indicator <- 1

# 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
habitatMask <- matrix(1, nrow = 4, ncol=4, byrow = TRUE)
# Create local objects 
ObsWindowsLocal <- getLocalObjects(habitatMask = habitatMask,
                                   coords = ScaledLowerCoords$coordsDataScaled,
                                   dmax=3,
                                   resizeFactor = 1,
                                   plot.check = TRUE
)
x <- c(1.1, 1.2)
windowIndex <- getWindowIndex(curCoords = x,
                              lowerCoords = ScaledLowerCoords$coordsDataScaled,
                              upperCoords =ScaledUpperCoords$coordsDataScaled)
x <- c(x, windowIndex)
dbernppLocalDetection_normal(x, ScaledLowerCoords$coordsDataScaled,
                             ScaledUpperCoords$coordsDataScaled,
                             s, sd, baseIntensities,  
                             ObsWindowsLocal$habitatGrid, ObsWindowsLocal$resizeFactor,
                             ObsWindowsLocal$localIndices,ObsWindowsLocal$numLocalIndices,
                             numWindows, indicator, log = TRUE)