Mathematical Sciences: Statistical Intervals

黄禹锡将研究统计领域的条件分析理论和以测量误差模型为基础的预测理论。在提案的第一部分中，首席研究员建议通过将估计置信度方法应用于Fieller问题并将其与Fisher对列联表的精确检验联系起来，来检验估计置信度方法。第二部分的研究将集中在基于测量误差模型的预测区间的构建上，这在许多应用中都有出现。基于无损检测的混凝土抗压强度预测问题是本课题主要研究对象。首席研究员将研究两个领域：条件推理和预测。对于第一个领域，黄禹锡将确定评估特定事件概率的统计程序比其他统计程序更能利用幸运数据；换句话说，哪些程序有条件地工作得更好。所涉及的事件是指一个特定的区间（基于数据）是否涵盖未知参数的某些比率。在第二个领域，黄禹锡将重点研究更适用于美国社会的“间隔预测”。本研究的目的是建立基于穿透声波脉冲速度等非破坏性方法的墙体、桥梁或建筑物抗压强度预测区间。这项工程的成功可能有助于在不破坏桥梁任何部分的情况下确定桥梁是否脆弱到值得关注的程度。

Hwang will work on two areas in statistics: a theory concerning the conditional analysis and a theory about prediction based on a measurement error model. In the first part of the proposal, the principal investigator proposes to examine the estimated confidence approach by applying it to the Fieller's problem and by relating it to Fisher's exact tests for contingency tables. The second part of the research will focus on construction of prediction intervals based on measurement error models, which arise in many applications. The examples that motivate the principal investigator in this research are about the prediction problems of compressive strengths of concrete based on nondestructive tests. The principal investigator will work on two areas: conditional inference and prediction. For the first area, Hwang shall determine which statistical procedures for evaluating the probability of a particular event can take advantage of lucky data better than others; in other words, which procedures work better conditionally. The event involved refers to whether a particular interval (based on data) covers some ratios of unknown parameters. In the second area, Hwang's focus will be on prediction by intervals, where the studies are more applicable to U.S. society. The aim of the research is to construct a prediction interval for the compressive strength of a wall, a bridge, or a building based on a nondestructive method such as pulse velocity of penetrating sound waves. Success of this project may help to determine, without destroying any part of the bridge, whether the bridge is weak enough that it causes concern.