Spatially Constrained Sampling

Abstract

Environmental epidemiology is a discipline that relies to a large extent on observational studies; even the case–control studies that are a standard tool of epidemiologists do not approach the rigor of the design of agricultural field trials. There is a very real tension in environmental epidemiology between the desire to establish a network of causation and the lack of experimental control available in observational studies. However, when the ‘signal’ is strong enough, sometimes it is possible to establish causative relationships. To make progress with noisy data and vaguely formulated hypotheses, statistical models have been developed that allow inference even down to individual levels, such as in frailty models. Many of these models are hierarchical and some are spatial, and it is on these that this article focuses.

Comparison of relative efficiencies of sampling plans excluding certain neighboring units: a simulation study

“…Thus, a corner unit like (1, 1) has L + M − 1 neighbors, which include all points in the same row, M, or same column, L, plus the diagonally adjacent point, (2,2). Other edge units, like (1,2), have L + M neighbors, and interior units like (2,2) have L + M + 2 neighbors.…”

“…( From the table, the unit from the first row could be (1, 1), (1, 2), (1, 3), (1, 4), or (1,5). Now, suppose we choose (1, 1) from the first row, then from the second row we cannot choose (2, 1) or (2, 2), because each is a neighbor of (1, 1).…”

“…Generally, spatially constrained sampling [1] accommodates some type of constraint in a spatial setting. As an example, consider estimating the number of distinct insect species (abundance) in a forest ecosystem.…”

Cyclic Polygonal Designs with Block Size 3 and Joint Distance α = 2

“…There were certain regions in the forest where a low insect count was expected from all trees due to recent fires, and other regions, near a creek, where a relatively high count was expected. Therefore, a sampling plan that avoids the simultaneous selection of neighboring plots within a region was utilized (See and Song, 2002).…”