The purpose of this research project is to develop new adaptive sampling designs and inference methods for sampling in network and spatially structured populations. Adaptive sampling designs are those in which the procedure for selecting the sample can depend on values of variables of interest observed during the survey. In spatial settings, that can mean adaptively adding new units to the sample in the vicinity of high or otherwise interesting observed values. In network or graph settings, links can be adaptively followed from interesting sample nodes to add new nodes to the sample. A variety of new sampling procedures, together with design and model based estimation methods, will be investigated in the study. A new, flexible and versatile class of adaptive designs, termed ``active set adaptive sampling,'' was found during the preliminary work toward this project. Designs in this class have certain advantages over adaptive cluster sampling and some of the traditional network sampling designs in being more flexible, allowing for control of total sample size and not requiring complete inclusion of connected components. Design-unbiased estimates are possible with some of these designs, providing inferences that are robust against assumptions about the population. These designs lend themselves toward model-based inferences as well and can be used in some situations to help ensure that the assumptions for the model-based inferences are met. This project will advance the theory and methodology of adaptive sampling and in particular will fully investigate and develop several categories of new adaptive sampling designs within this class and develop and evaluate design and model based inference methods for use with adaptive designs of all types.
With adaptive sampling designs, the study design can change in response to the values and patterns observed during the study. For example, in a study of an at-risk hidden human population, social links from particularly high-risk individuals can be followed to add more individuals to the sample; in a survey of an unevenly distributed natural resource, new observations may be adaptively made in neighborhoods of high observed abundance. In previous work it has been established that in many situations the theoretically optimal sampling strategy is an adaptive one. Specific adaptive designs, such as the adaptive cluster sampling designs developed in a previous project, have been shown to give substantial gains in precision or efficiency over conventional strategies for certain types of populations, in particular rare, clustered ones. The results of the proposed research will provide research tools for other scientific fields, including the biological, environmental, health, and social sciences. Each of these fields has to deal with populations that are difficult to sample by conventional means because of their unpredictably uneven spatial and network structures. The sampling methods resulting from this project have applications to many situations of importance to society, including studies of hidden populations such as those at risk for HIV/AIDS, environmental assessment and monitoring, biological surveys, natural resources explorations and inventories, Internet surveys, rapid response to natural and induced health threats, studies in human social behavior, and archaeological studies.
