dpoisppLocalDetection_normal {nimbleSCR}

Local evaluation for a Poisson point process detection model

Description

Density and random generation functions of the Poisson point process for detection. The dpoisppLocalDetection_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

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

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

Arguments

x

Matrix 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.

habitatGridLocal

Matrix of rescaled habitat grid cells indices, from localIndices returned by the getLocalObjects function (

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 rescaled habitat grid cell, as returned by the getLocalObjects function (object named localIndices).

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.

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

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

Author(s)

Wei Zhang, Cyril Milleret and Pierre Dupont

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)$coordsDataScaled ScaledUpperCoords <- scaleCoordsToHabitatGrid(coordsData = upperCoords, coordsHabitatGridCenter = coordsHabitatGridCenter)$coordsDataScaled ScaledUpperCoords[,2] <- ScaledUpperCoords[,2] + 1.5 ScaledLowerCoords[,2] <- ScaledLowerCoords[,2] - 1.5 habitatMask <- matrix(1, nrow = 4, ncol=4, byrow = TRUE) # Create local objects ObsWindowsLocal <- getLocalObjects(habitatMask = habitatMask, coords = ScaledLowerCoords, dmax=3, resizeFactor = 1, plot.check = TRUE )

# Detection locations x <- matrix(c(1.5, 2, 1.1, 1.5, 1.4, 0.7, 2, 1.3, 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, upperCoords =ScaledUpperCoords) x <- cbind(x, windowIndexes) # get the total number of detections on x[1,1] x <- rbind(c(length(windowIndexes),0,0), x) dpoisppLocalDetection_normal(x, ScaledLowerCoords, ScaledUpperCoords, s, sd, baseIntensities, ObsWindowsLocal$habitatGrid, ObsWindowsLocal$resizeFactor, ObsWindowsLocal$localIndices,ObsWindowsLocal$numLocalIndices, numMaxPoints = dim(x)[1], numWindows, indicator, log = TRUE)