Description Usage Arguments Details Value Author(s) References Examples
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.
1 |
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 |
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.
prob |
Probability of patch detection |
ssize |
Sample size |
rad |
Patch radius |
sep |
Separation distance (for square and triangular lattice designs) |
Jon Barry: Jon.Barry@cefas.co.uk
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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | 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))
|
[1] 0.8665933
[1] 22.3079
[1] 2.400534
$prob
[1] 0.8760176
$ssize
[1] 15
$rad
[1] 1.4
$sep
[1] 2.581989
$prob
[1] 0.6
$ssize
[1] 9.74418
$rad
[1] 1.4
$sep
[1] 3.203519
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