Mathematical Sciences: Statistical Intervals

Hwang将在统计学的两个领域开展工作：关于条件分析的理论和关于基于测量误差模型的预测的理论。在提案的第一部分，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，来检查估计置信度方法。第二部分的研究将集中于基于测量误差模型的预测区间的构建，这些模型在许多应用中都会出现。在这项研究中激励主要研究者的例子是关于基于无损试验的混凝土抗压强度的预测问题。首席研究员将在两个领域开展工作：条件推理和预测。对于第一个领域，Hwang应确定评估特定事件概率的哪些统计程序可以比其他程序更好地利用幸运数据；换句话说，哪些程序有条件地工作得更好。所涉及的事件是指特定间隔(基于数据)是否覆盖未知参数的某些比率。在第二个领域，Hwang的重点将是按区间预测，这方面的研究更适用于美国社会。该研究的目的是基于非破坏性方法(如穿透声波的脉冲速度)来构建墙、桥或建筑物的抗压强度的预测区间。该项目的成功可能有助于在不破坏大桥任何部分的情况下确定大桥是否足够脆弱，从而引起人们的担忧。

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.