Adaptive Sampling Designs in Network and Spatial Settings

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The purpose of this research project is to develop new adaptivesampling designs and inference methods for sampling in network andspatially structured populations. Adaptive sampling designs are thosein which the procedure for selecting the sample can depend on valuesof variables of interest observed during the survey. In spatialsettings, that can mean adaptively adding new units to the sample inthe vicinity of high or otherwise interesting observed values. Innetwork or graph settings, links can be adaptively followed frominteresting sample nodes to add new nodes to the sample. A variety ofnew sampling procedures, together with design and model basedestimation methods, will be investigated in the study. A new,flexible and versatile class of adaptive designs, termed ``active setadaptive sampling,'' was found during the preliminary work toward thisproject. Designs in this class have certain advantages over adaptivecluster sampling and some of the traditional network sampling designsin being more flexible, allowing for control of total sample size andnot requiring complete inclusion of connected components.Design-unbiased estimates are possible with some of these designs,providing inferences that are robust against assumptions about thepopulation. These designs lend themselves toward model-basedinferences as well and can be used in some situations to help ensurethat the assumptions for the model-based inferences are met. Thisproject will advance the theory and methodology of adaptive samplingand in particular will fully investigate and develop severalcategories of new adaptive sampling designs within this class anddevelop and evaluate design and model based inference methods for usewith adaptive designs of all types.With adaptive sampling designs, the study design can change inresponse to the values and patterns observed during the study. Forexample, in a study of an at-risk hidden human population, sociallinks from particularly high-risk individuals can be followed to addmore individuals to the sample; in a survey of an unevenly distributednatural resource, new observations may be adaptively made inneighborhoods of high observed abundance. In previous work it hasbeen established that in many situations the theoretically optimalsampling strategy is an adaptive one. Specific adaptive designs, suchas the adaptive cluster sampling designs developed in a previousproject, have been shown to give substantial gains in precision orefficiency over conventional strategies for certain types ofpopulations, in particular rare, clustered ones. The results of theproposed research will provide research tools for other scientificfields, including the biological, environmental, health, and socialsciences. Each of these fields has to deal with populations that aredifficult to sample by conventional means because of theirunpredictably uneven spatial and network structures. The samplingmethods resulting from this project have applications to manysituations of importance to society, including studies of hiddenpopulations such as those at risk for HIV/AIDS, environmentalassessment and monitoring, biological surveys, natural resourcesexplorations and inventories, Internet surveys, rapid response tonatural and induced health threats, studies in human social behavior,and archaeological studies.