Mathematical Sciences: Adaptive Sampling

本研究旨在发展自适应抽样设计的理论与方法。该方法包括确定最优自适应设计的理论发展和比较实际自适应设计与非自适应设计的计算机模拟的结合。利用总体的条件均方误差结构，提出了设计诱导无偏性，以提供对可能偏离关于总体的假设的稳健性。为了检验一类重要的自适应设计，提出了聚集点过程实现的模拟抽样。本研究属于实验设计的子领域，属于统计学的一般领域。目的是通过发展设计实验的理论来更有效地利用实验中的信息，以便可以根据可能顺序依赖于先前选择的单元的观察的规则从总体中抽样实验单元。在这一方向上取得的重大进展有可能使科学实验的实践发生革命性的变化，并使我们的国家研究和发展资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.