B. L. Robertson

BAS: balanced acceptance sampling of natural resources.

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 cover partitioning method for bound constrained global optimization

A stochastic algorithm for global optimization subject to simple bounds is described. The method is applicable to black-box functions which may be non-smooth or discontinuous. The algorithm is in the spirit of the deterministic algorithm direct of Jones, Perttunen, and Stuckman. Like direct, it generates successively finer covers of the feasible region, where each cover consists of a finite number of boxes, and each box is defined by simple bounds. Its principal difference is that it calculates the objective at a randomly selected point in each unpopulated box, rather than at the centre of the box. A limited storage version of the algorithm is also presented. The sequence of best-known function values is shown to converge to the essential minimum with probability 1 for both versions of the algorithm. A worst case expected rate theorem is established. Numerical results are presented which show the methods are effective in practice.

A CARTopt method for bound constrained global optimization

A stochastic algorithm for bound-constrained global optimization is described. The method can be applied to objective functions that are nonsmooth or even discontinuous. The algorithm forms a partition on the search region using classification and regression trees (CART), which defines a region where the objective function is relatively low. Further points are drawn directly from the low region before a new partition is formed. Alternating between partition and sampling phases provides an effective method for nonsmooth global optimization. The sequence of iterates generated by the algorithm is shown to converge to an essential global minimizer with probability one under mild conditions. Nonprobabilistic results are also given when random sampling is replaced with points taken from the Halton sequence. Numerical results are presented for both smooth and nonsmooth problems and show that the method is effective and competitive in practice. 2010 Mathematics subject classification: 90C26.

Using balanced acceptance sampling as a master sample for environmental surveys

Environmental management agencies rely on the results of monitoring to answer questions about the success of their policies and programmes. Monitoring is often designed to address information needs for a particular site or small set of sites. If the study is poorly designed, it can fail to provide meaningful data to inform management and policy decision making (Field, O’Connor, Tyre, & Possingham, 2007; Legg & Nagy, 2006; Nichols & Williams, 2006). Extrapolating from these studies to answer larger scale questions can bias the estimates as single sites are rarely representative of a broader region (Dixon, Olsen, & Kahn, 1998; Peterson, Urquhart, & Welch, 1999). Increasingly, monitoring on a large scale is needed to inform management needs and assess progress towards targets concerned with global biodiversity change (Buckland, Magurran, Green, & Fewster, 2005; Magurran et al., 2010; Noss, 1999; Pereira & Cooper, 2006). Monitoring objectives and sample areas of national, regional, and local agencies often overlap creating efficiencies if the different groups coordinate their effort. Coordinating requires consistent formulation of goals and objectives, selection of indicators and measures, field Received: 22 November 2017 | Accepted: 5 March 2018 DOI: 10.1111/2041-210X.13003

Halton iterative partitioning: spatially balanced sampling via partitioning

A new spatially balanced sampling design for environmental surveys is introduced, called Halton iterative partitioning (HIP). The design draws sample locations that are well spread over the study area. Spatially balanced designs are known to be efficient when surveying natural resources because nearby locations tend to be similar. The HIP design uses structural properties of the Halton sequence to partition a resource into nested boxes. Sample locations are then drawn from specific boxes in the partition to ensure spatial diversity. The method is conceptually simple and computationally efficient, draws spatially balanced samples in two or more dimensions and uses standard design-based estimators. Furthermore, HIP samples have an implicit ordering that can be used to define spatially balanced over-samples. This feature is particularly useful when sampling natural resources because we can dynamically add spatially balanced units from the over-sample to the sample as non-target or inaccessible units are discovered. We use several populations to show that HIP sampling draws spatially balanced samples and gives precise estimates of population totals.