Adaptive Sampling Designs in Network and Spatial Settings

本研究项目的目的是为网络和空间结构群体的采样开发新的自适应采样设计和推理方法。自适应抽样设计是指选择样本的程序可以取决于在调查期间观察到的感兴趣变量的值。在空间设置中，这可能意味着在高或其他有趣的观测值附近自适应地向样本添加新单位。在网络或图形设置中，可以自适应地跟踪感兴趣的样本节点的链接，以便向样本中添加新节点。各种新的抽样程序，以及基于设计和模型的估计方法，将在研究中进行调查。在该项目的初步工作中，发现了一种新的、灵活的、通用的自适应设计，称为“主动集自适应采样”。与自适应聚类抽样和一些传统的网络抽样设计相比，这类设计具有一定的优势，即更灵活，允许控制总样本大小，并且不需要完全包含连接的组件。设计无偏估计是可能的，其中一些设计提供了对人口假设的稳健推断。这些设计也适用于基于模型的推断，并且可以在某些情况下用于帮助确保满足基于模型的推断的假设。该项目将推进自适应采样的理论和方法，特别是将充分调查和开发本课程中几种新的自适应采样设计，并开发和评估用于所有类型的自适应设计的基于设计和模型的推理方法。采用自适应抽样设计，研究设计可以根据研究期间观察到的值和模式而改变。例如，在一项对有风险的隐藏人群的研究中，可以根据来自特别高风险个体的社会联系将更多的个体纳入样本；在对分布不均匀的自然资源进行调查时，可以自适应地在观测到的丰度高的邻近区域进行新的观测。在以前的工作中已经确定，在许多情况下，理论上最优的采样策略是自适应的。特定的自适应设计，如在以前的项目中开发的自适应聚类抽样设计，已被证明在某些类型的种群，特别是罕见的，聚类的群体中，比传统策略在精度和效率方面有实质性的提高。拟议研究的结果将为其他科学领域提供研究工具，包括生物、环境、健康和社会科学。这些领域中的每一个都必须处理由于其不可预测的不均匀空间和网络结构而难以用传统方法采样的人群。该项目产生的抽样方法可应用于对社会有重要意义的许多情况，包括对艾滋病毒/艾滋病风险人群等隐藏人群的研究、环境评估和监测、生物调查、自然资源勘探和清查、互联网调查、自然和诱发健康威胁的快速反应、人类社会行为研究和考古研究。

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.