Sampling (infinite) populations in a geospatial framework: an operational perspective

Several approaches have been proposed when selecting samples heterogeneously distributed over space. In a monodimensional field, Quenouille (1949) has demonstrated how systematic sampling is an optimal design aimed at delineating the most spread sample with equal inclusion probability. In this perspective a basic and well- known family of operational approaches consists of transforming a multidimensional sampling problem into a one-dimensional exercise to apply a systematic design. This is, for instance, the case of a stratified sampling method operationalized by a generalized random tessellation (Stevens and Olsen, 1999, 2003, 2004). They used a quadrant-recursive partition of the unit square to map itto shift toward a one- dimensional problem. At the same time and from different methodological perspectives, Dickson and Tillé (2016) have used the traveling salesman problem to reduce the sampling problem to one dimension.