Mathematical Sciences: Adaptive Sampling

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Adaptive sampling designs are designs in which the procedure for selecting the units to include in the sample may depend on observed values of the variable of interest. In previous research supported by NSF grants DMS-8705812 and DMS-9016708, the methodology of adaptive sampling was advanced to the point where now there are a number of practical adaptive designs, giving remarkably high efficiencies for sampling rare, clumped, or aggregated populations compared to conventional designs of equivalent sample size. Theoretical results suggest, however, that greater potential still exists. It is proposed to further develop the basic theory of adaptive sampling and look for new classes of adaptive sampling designs. Adaptive sampling designs are designs in which the procedure for selecting the units or sites to include in the sample depends on observations made during the survey. For example, in a survey to estimate the abundance of a rare animal species, additional observations may be made in the vicinity of sites with high observed abundance. In a survey of an environmental pollutant, additional observations may be made in the vicinity of discovered ``hot spots.'' For such surveys, adaptive sampling designs can provide estimates of far greater precision than can be obtained with conventional designs of equivalent sampling effort. Research is proposed to develop the theory and methods of adaptive sampling. The proposed research has immediate, important applications to many fields, including environmental, ecological, and natural resource studies.