Spatially Balanced Sampling through the Pivotal Method

Abstract

A simple method to select a spatially balanced sample using equal or unequal inclusion probabilities is presented. For populations with spatial trends in the variables of interest, the estimation can be much improved by selecting samples that are well spread over the population. The method can be used for any number of dimensions and can hence also select spatially balanced samples in a space spanned by several auxiliary variables. Analysis and examples indicate that the suggested method achieves a high degree of spatial balance and is therefore efficient for populations with trends.

How to find simple nonlocal stability and resilience measures

“…Indeed, we have to sample a relatively large number of initial conditions in order to get a "good enough covering" of the desired part of the state-space, as well as small enough variances of our estimates, and each sampled trajectory is expensive in terms of computational time. In this section, we will show how the local pivotal method by Grafström et al [22] easily can be applied in order to sample well-spread sets of initial conditions. This results in efficient variance reduction of our estimates, and thus less initial conditions need to be tested, resulting in shorter computational time.…”

“…In Sect. 3.2, we explain a simple way to achieve this by using the local pivotal method by Grafström et al [22] when sampling the perturbations.…”

A modification of balanced acceptance sampling

“…, N } is the sample and π i is the inclusion probability of the ith unit. The variance ofτ can be estimated using the Sen-Yates-Grundy estimator (Yates & Grundy, 1953), but this estimator is biased and tends to be unstable for spatially-balanced designs (Grafström et al, 2012;Robertson et al, 2013). The local mean variance estimator (Stevens & Olsen, 2003) is commonly used for spatially balanced designs and is recommended for the modified BAS approach.…”

“…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).…”

A Cost-Constrained Sampling Strategy in Support of LAI Product Validation in Mountainous Areas

“…Since nearby measurements are more similar than measurements further apart, which is common in the real world, then it is advantageous to make sure that the sampling plots are as spread as possible to mitigate the information redundancy [44]. NNI was calculated to evaluate the representativeness in geographic space.…”