BAS: Balanced Acceptance Sampling of Natural Resources

Abstract

To design an efficient survey or monitoring program for a natural resource it is important to consider the spatial distribution of the resource. Generally, sample designs that are spatially balanced are more efficient than designs which are not. A spatially balanced design selects a sample that is evenly distributed over the extent of the resource. In this article we present a new spatially balanced design that can be used to select a sample from discrete and continuous populations in multi-dimensional space. The design, which we call balanced acceptance sampling, utilizes the Halton sequence to assure spatial diversity of selected locations. Targeted inclusion probabilities are achieved by acceptance sampling. The BAS design is conceptually simpler than competing spatially balanced designs, executes faster, and achieves better spatial balance as measured by a number of quantities. The algorithm has been programed in an R package freely available for download.

A modification of balanced acceptance sampling

“…In this section we modify the original BAS design of Robertson et al (2013) and show how the modified design achieves exact equi-probable samples from Halton frames. For simplicity, the modified design uses a random-start in the Targeted inclusion probabilities are not necessarily achieved with BAS because a variable number of BAS points are rejected for not selecting a unit at the very beginning of the sequence.…”

“…Natural resources are often spatially autocorrelated because nearby locations interact with one another and are influenced by the same factors (Stevens & Olsen,5 2004). Hence, spreading the sample over of the study area is known to be efficient, and many variations of spatially balanced designs have been proposed (Stevens & Olsen, 2004;Grafström et al, 2012;Robertson et al, 2013). This article considers balanced acceptance sampling (BAS) (Robertson et al, 2013).…”

“…In particular, BAS uses a random-start Halton sequence (Wang & Hickernell, 2000), which maps the natural numbers to vectors {x k } ∞ k=1 in [0, 1) d (Robertson et al, 2013). The ith coordinate of each vector in the sequence has an associated base, b i , and all bases {b 1 , b 2 , .…”

“…This process of testing successive points for membership in Ω is repeated until the required number of points has been accepted. Unequal probability samples can be achieved by adding a dimension and using an acceptance/rejection sampling strategy (Robertson et al, 2013).…”

“…If the Halton frame is not used, targeted inclusion probabilities may not be achieved exactly using the modified BAS approach, but can be estimated using the approaches described in (Robertson et al, 2013). Consider drawing equi-probable BAS samples from a discretization (see Figure 3) of the northern part of New Zealand's South Island (this is not a Halton frame).…”