Spatially balanced sampling designs for environmental surveys.

Some environmental studies use non-probabilistic sampling designs to draw samples from spatially distributed populations. Unfortunately, these samples can be difficult to analyse statistically and can give biased estimates of population characteristics. Spatially balanced sampling designs are probabilistic designs that spread the sampling effort evenly over the resource. These designs are particularly useful for environmental sampling because they produce good-sample coverage over the resource, they have precise design-based estimators and they can potentially reduce the sampling cost. The most popular spatially balanced design is Generalized Random Tessellation Stratified (GRTS), which has many desirable features including a spatially balanced sample, design-based estimators and the ability to select spatially balanced oversamples. This article considers the popularity of spatially balanced sampling, reviews several spatially balanced sampling designs and shows how these designs can be implemented in the statistical programming language R. We hope to increase the visibility of spatially balanced sampling and encourage environmental scientists to use these designs.

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 comparison of design-based and model-based approaches for finite population spatial sampling and inference.

The design-based and model-based approaches to frequentist statistical inference rest on fundamentally different foundations. In the design-based approach, inference relies on random sampling. In the model-based approach, inference relies on distributional assumptions. We compare the approaches in a finite population spatial context.We provide relevant background for the design-based and model-based approaches and then study their performance using simulated data and real data. The real data is from the United States Environmental Protection Agency's 2012 National Lakes Assessment. A variety of sample sizes, location layouts, dependence structures, and response types are considered. The population mean is the parameter of interest, and performance is measured using statistics like bias, squared error, and interval coverage.When studying the simulated and real data, we found that regardless of the strength of spatial dependence in the data, the generalized random tessellation stratified (GRTS) algorithm, which explicitly incorporates spatial locations into sampling, tends to outperform the simple random sampling (SRS) algorithm, which does not explicitly incorporate spatial locations into sampling. We also found that model-based inference tends to outperform design-based inference, even for skewed data where the model-based distributional assumptions are violated. The performance gap between design-based inference and model-based inference is small when GRTS samples are used but large when SRS samples are used, suggesting that the sampling choice (whether to use GRTS or SRS) is most important when performing design-based inference.There are many benefits and drawbacks to the design-based and model-based approaches for finite population spatial sampling and inference that practitioners must consider when choosing between them. We provide relevant background contextualizing each approach and study their properties in a variety of scenarios, making recommendations for use based on the practitioner's goals.

Active regional surveillance for early detection of exotic/emerging pathogens of swine: A comparison of statistical methods for farm selection.

In this study, five spatially balanced sampling methods, i.e., generalized random-tessellation stratified (GRTS), local pivotal method (LPM), spatially correlated Poisson sampling (SCPS), local cube method (LCUBE), and balanced acceptance sampling (BAS) were compared to simple random sampling (SRS) based on a livestock disease transmission model on a hypothetical region (195 km × 300 km) populated with 6000 farms in terms of the probability of detection by sample size. Given a fixed sample size, four of the five spatially balanced sampling methods provided better performance than SRS, i.e., higher probabilities of detecting at least one infected farms over a range of regional prevalence evaluated (1%-5%). That is, for any given probability of detection, spatially balanced methods required testing fewer farms than SRS. In an era of pandemics, active regional surveillance for early detection of emerging pathogens becomes urgent, yet shrinking budgets impose intractable constraints. The better performance and higher efficiency of spatially balanced sampling methods suggests a potential improvement in regional livestock disease surveillances and a partial solution to the challenge of affordable surveillance.