Optimal adaptive selection of sampling sites

Under an assumed population model, the optimal sampling strategy is often an adaptive one. In spatial statistics an important problem is that of optimally locating sample sites for estimation or prediction. In some cases a certain number of sampling sites have already been located and now one would like to optimally choose locations for a set of additional sites. If the optimal strategy is an adaptive one, then the selection of the new sites should take into account not only the locations of the existing sites but also the values of the variable of interest observed at those sites. In this paper, the optimal sampling strategy in two phases is examined and compared with the optimal conventional strategy. While the optimal conventional design is approximately a systematic arrangement of sampling sites, the optimal adaptive selection varies depending on the realized spatial distribution. The relative efficiency of the optimal (adaptive) strategy to the optimal conventional strategy, which is always greater than 1, is seen to be related to the range of influence of the spatial covariance function. Finally, the strategies are compared using data from a study of geothermal with CO₂ emissions in Yellowstone National Park.