Adaptive Sampling Designs in Network and Spatial Settings

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.