Mathematical Sciences: Adaptive Sampling

自适应抽样设计是这样一种设计，在该设计中，选择要包括在样本中的单位的程序可以取决于感兴趣变量的观测值。在之前由美国国家科学基金会资助的研究中，自适应抽样的方法已经发展到了现在有许多实用的自适应设计的地步，与同等样本量的传统设计相比，对稀有、聚集或聚集种群的抽样具有非常高的效率。然而，理论结果表明，更大的潜力仍然存在。建议进一步发展自适应抽样的基本理论，寻找新的自适应抽样设计。自适应抽样设计是这样一种设计，在这种设计中，选择纳入样本的单位或地点的程序取决于调查期间的观察。例如，在一项估计稀有动物物种丰度的调查中，可能会在观测到的丰度较高的地点附近进行额外的观测。在环境污染物调查中，可以在发现的“热点”附近进行额外的观测。对于这类调查，自适应抽样设计可以提供比同等抽样工作量的常规设计所能获得的估计精度高得多的估计。提出了发展自适应抽样的理论和方法的研究。拟议的研究在许多领域都有直接、重要的应用，包括环境、生态和自然资源研究。

Adaptive sampling designs are designs in which the procedure for selecting the units to include in the sample may depend on observed values of the variable of interest. In previous research supported by NSF grants DMS-8705812 and DMS-9016708, the methodology of adaptive sampling was advanced to the point where now there are a number of practical adaptive designs, giving remarkably high efficiencies for sampling rare, clumped, or aggregated populations compared to conventional designs of equivalent sample size. Theoretical results suggest, however, that greater potential still exists. It is proposed to further develop the basic theory of adaptive sampling and look for new classes of adaptive sampling designs. Adaptive sampling designs are designs in which the procedure for selecting the units or sites to include in the sample depends on observations made during the survey. For example, in a survey to estimate the abundance of a rare animal species, additional observations may be made in the vicinity of sites with high observed abundance. In a survey of an environmental pollutant, additional observations may be made in the vicinity of discovered ``hot spots.'' For such surveys, adaptive sampling designs can provide estimates of far greater precision than can be obtained with conventional designs of equivalent sampling effort. Research is proposed to develop the theory and methods of adaptive sampling. The proposed research has immediate, important applications to many fields, including environmental, ecological, and natural resource studies.