detect {emon} | R Documentation |
Probability of circular patch detection
Description
The function can calculate the probability of detection of a circular patch of specified radius for a specified density of points; the density needed to achieve a specified probability of detection; or the radius of the patch that will be detected with specified probability and sampling density.This is done for random, square lattice, and triangular lattice spatial sampling designs.
Usage
detect(method, statistic, area=NA, radius=NA, pdetect=NA, ssize=NA)
Arguments
method |
Defines the spatial sampling design to be used. The values can be |
statistic |
Describes what aspect of design you want calculated. The choices are |
area |
The survey area (same units as distance and radius). |
radius |
Patch radius. Not needed if |
pdetect |
Probability detection. Not needed if |
ssize |
Sample size. Not needed if |
Details
The basic idea is that you wish to conduct a survey in an area area
to detect some object (patch) of
interest. This could be a cockle patch, an area of reef or an archaeological deposit. This function asssumes that
the object is circular with radius radius
. You have three choices of sampling deign to use: spatial, square
lattice and triangular lattice. In terms of patch detection, for a given sample size, the triangular design gives
the highest probability - because its points are equi-distant apart.
The simplest application of this function is to assess the patch detection probability for a particular design. This
is obtained using the statistic="P"
option. However, the problem can be turned around and this function used to
calculate the sample size needed to obatain a specific patch detection probability (statistic="N"
) or the radius
of the patch that would be detected with some desired probability (statistic="R"). Th
is last scenario might be
useful if there was some particular size of patch that you wanted to be sure (say, 90 percent) of detecting.
Value
prob |
Probability of patch detection |
ssize |
Sample size |
rad |
Patch radius |
sep |
Separation distance (for square and triangular lattice designs) |
Author(s)
Jon Barry: Jon.Barry@cefas.co.uk
References
Barry J and Nicholson M D (1993) Measuring the probabilities of patch detection for four spatial sampling schemes. Journal of Applied Statistics, 20, 353-362.
Examples
detect(method='R', statistic='P', area=100, radius=2, ssize=15)$prob
detect(method='R', statistic='N', area=100, radius=2, pdetect=0.95)$ssize
detect(method='R', statistic='R', area=100, pdetect=0.95, ssize=15)$rad
detect(method='S', statistic='P', area=100, radius=1.4, ssize=15)
detect(method='S', statistic='N', area=100, radius=1.4, pdetect=0.6)
# Plot patch detection as a function of radius
square = rep(0,200); rand = square; triang = rand
radius = seq(0.01, 2, 0.01)
for (j in 1:200) {
rand[j] = detect(method='R', statistic='P', area=100, radius=radius[j], ssize=15)$p
square[j] = detect(method='S', statistic='P', area=100, radius=radius[j], ssize=15)$p
triang[j] = detect(method='T', statistic='P', area=100, radius=radius[j], ssize=15)$p
}
plot(radius, rand, ylim=c(0,1), xlab='Patch radius', ylab='Probability detection', type='l')
lines(radius, square, col=2, lty=2)
lines(radius, triang, col=3, lty=3)
legend('topleft', legend=c('Random', 'Square', 'Triangular'), col=c(1,2,3), lty=c(1,2,3))