Geoscience Reference
In-Depth Information
selected primary units. Then, in the second phase, additional units are allo-
cated to the primary units in proportion to the number of observed units
in that primary unit that exceed a threshold value
g
i
λ, where
g
i
is the num-
ber of sampled units in the
i
ith primary unit that exceed the threshold value
and λ is a multiplier. In two-stage sequential sampling (Salehi and Smith,
2005), the number of additional units allocated to the primary units is set
at some fixed value. The predefined threshold that triggers adaptive alloca-
tion can be the value of the observed unit
y
i
or some auxiliary information
related to
y
i
(Panahbehagh et al., 2011). For surveying a rare and clustered
population, these designs allow the survey effort to be intensified at the loca-
tions where the population is found. The results of comparative simulation
surveys showed gains in survey efficiency (measured by a reduced sample
variance) when the adaptive component was added to the conventional two-
stage design (Brown et al., 2008; Salehi et al
.
, 2010; Smith et al
.
, 2011).
In complete allocation stratified sampling, adaptive sampling is applied
to a conventional stratified or two-stage design (Salehi and Brown, 2010).
Starting with a conventional stratified design, if any unit in a stratum has
a value that exceeds a threshold, the stratum is completely surveyed. This
design simplifies adaptive sampling in two ways: First, the rule to decide
whether a stratum is to be allocated additional survey effort does not require
the first-phase survey in the stratum to be completed. Second, the instruc-
tions to the field crew about how much additional effort is required are sim-
ply to survey the entire stratum.
The complete allocation stratified design uses the best features of some of
the previous adaptive designs. Adaptive cluster sampling has considerable
intuitive appeal to a field biologist in surveys of rare and clustered popula-
tions because once a rare plant or animal is found, the neighboring area is
sampled. In complete allocation, the neighboring area is completely searched,
and what is considered the neighboring area is defined prior to sampling
and constrained by the stratum boundary. In adaptive cluster sampling, the
neighborhood is not defined prior to sampling and, for some populations,
can be excessively large (Brown, 2003).
The estimate of the population total for complete allocation stratified sam-
pling is
γ
∗
∑
y
ˆ
τ=
h
(3.5)
π
h
h
1
=
where
∗
y
h
is the total of the
y
values in the
h
th stratum, γ is the number of
strata that were completely surveyed, and π
h
is the probability the whole
stratum
h
is selected, which is
Nm
n
N
n
−
h
h
h
π= −
1
/
.
(3.6)
h
h
h
