Geoscience Reference
In-Depth Information
4.3 The Detection Function
The foremost component in the analysis of line transect data is the estima-
tion of a detection function. This function, which is denoted here by
g
(
x
),
gives the probability of detection of an object at a perpendicular distance
x
from the transect line. From assumption 1 provided in the preceding section,
g
(0) = 1.0
because the probability is 1.0 that an object with
x
= 0 will be detected. The
detection function therefore has a form like that shown in Figure 4.2 for the
particular example of a half-normal detection function (the positive half of
a normal distribution density function) scaled to have a height of
g
(
x
) = 1.0
when
x
= 0.
From assumptions 1 to 6, it can be shown that the average probability of
detection for an object in the strip of width 2
w
is estimated by
ˆ
ˆ
(0)}
=
P f
1/{
(4.1)
w
where
f
(
x
) denotes the probability density function for the observed distances
x
. To make use of this equation, the function
f
(
x
) is estimated by a curve
fitted to the relative frequency histogram of observed
x
values, and
ˆ
(0)
is
estimated by the intersection of
f
(
x
) with the vertical axis at
x
= 0, as shown
1.0
0.8
0.6
0.4
0.2
0
20
40
60
80
Distance from Line,
x
FIGURE 4.2
Graph of the half-normal probability-of-detection curve. Units on the horizontal axis are arbi-
trary. The height of the curve
g
(
x
) has been scaled so that
g
(0) = 1.0.
