Spatial Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 173

Fig. 7.5 Sample selected with DUST method

measure of distance between unit k and l . This rule can be easily extended to follow
the

classical exponential decreasing autocorrelation function

without losing the basic features of the selection algorithm.
Clearly at each step, the updated inclusion probabilities should be normalized to
sum to one. As a consequence, even the starting probabilities

ðÞ
l

ð l 1 e ʻd kl t 1

π ¼ π

ð 0 l should have sum
equal to 1. It is interesting that the author suggested that several parameters (

π

)
should be estimated using some auxiliary information, to obtain a list of discretized
distances. This is approximately the same as the suggestion to carefully estimate the
semivariogram, drawing on the motivations described in Sect. 7.2 .
This algorithm, or at least the sampling design that it implies, can easily be
interpreted and analyzed in a design-based perspective, with particular reference to
a detailed empirical assessment of the first and second-order inclusion probabilities
because they are theoretically unknown (see Sect. 7.7 ).
There is no package in R with a function to implement this selection method.
However, this task is not difficult because its draw-by-draw nature makes it easy to
develop an additional user defined function. The selected sample is shown in
Fig. 7.5 .

ʻ