Halton iterative partitioning master frames

A spatial sampling design determines where sample locations are placed in a study area. To achieve reliable estimates of population characteristics, the spatial pattern of the sample should be similar to the underlying spatial pattern of the population. A reasonable assumption for natural resources is that nearby locations tend to have more similar response values than distant locations. Hence, sample efficiency can be increased by spreading sample locations evenly over a natural resource. A sample that is well-spread over the resource is called spatially balanced and many spatially balanced sampling designs have been proposed in the statistical literature. Robertson et al. (Environ Ecol Stat 25:305–323, 2018) proposed a sampling design that draws spatially balanced samples using a nested partition. This article modifies their partitioning strategy to spatially order a point resource into a highly structured master frame. Samples of consecutive points from the master frame are spatially balanced and these individual samples can be easily incorporated into a broader spatially balanced design for integrated monitoring. Numerical results show that the master frame’s ordering is effective and that a range of samples drawn from it are spatially balanced.