Mathematical Sciences: Adaptive Sampling

本研究旨在发展自适应抽样设计的理论与方法。所提出的方法包括理论发展来确定最优的自适应设计和计算机模拟来比较实际的自适应设计和非自适应设计。利用总体的条件均方误差结构，设计诱导无偏性被提出，以提供对可能偏离总体假设的鲁棒性。提出了对聚类点过程实现的模拟采样，以检验一类重要的自适应设计。这项研究是在实验设计的子领域，在统计的一般领域。目标是通过发展设计实验的理论，更有效地利用实验中的信息，以便根据可能依赖于先前选择的单位的观察顺序的规则，从总体中抽样实验单位。在这个方向上取得重大进展具有长期潜力，可以彻底改变科学实验的做法，并使我们的国家研究和发展基金得到更有效的利用。

This research is to develop the theory and methodology of adaptive sampling designs. The proposed approach involves a combination of theoretical development to determine optimal adaptive designs and computer simulation to compare practical adaptive designs with non adaptive ones. Taking advantage of the conditional mean square error structure of the population, design-induced unbiasedness is proposed to provide robustness against possible departures from assumptions about populations. Simulated sampling of cluster point process realizations is proposed to examine one important class of adaptive designs. This research is in the subfield of experimental design, in the general area of statistics. The goal is to utilize the information in an experiment more efficiently by developing the theory of designing experiments so that experimental units may be sampled from a population according to rules that may depend sequentially on observations of previously selected units. Significant progress in this direction has the long term potential for revolutionizing the practice of scientific experimentation and providing for more efficient use of our national research and development funds.