Adaptive sampling in space and time

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The proposed research develops theory and methods of adaptive sampling in space and time.  Adaptive sampling designs are those in which the selection of the sample units depends on values of variables of interest observed during the course of the survey.  Adaptive designs can offer substantial increases in efficiency for spatially clustered, rare, and networked populations. One area of the proposed research investigates and develops adaptive sampling designs in which the sampling units may move during the course of the survey.  For sampling spatially distributed populations, a sampling unit is typically conceived to be a fixed point or subset of the region of interest.  For populations distributed in space and time, however, it makes sense to consider sampling paths on which units move through space over time.  In this case, a sampling unit is a path, manifold, or subregion in space/time.  For example, to monitor for surprise releases of acute air pollutant clouds with a limited number of sensor units, it is most efficient to have units moving in paths that are predominantly perpendicular to the wind.  Similar path considerations may apply to surveys of migratory animals using boats or aircraft.  More complex dynamic sampling plans apply to designs for monitoring the progress of epidemics through social networks.  Adaptive moving designs in which the paths can change or new paths be added in response to observed values will be investigated. Other areas of the proposed research programme include adaptive interventions or experiments in natural and human populations, theory of adaptive designs, and new adaptive designs to take advantage of special population structures.  The proposed research has important applications to the health and environmental sciences and other fields.