Constrained Nonparametric Inference and Data Visualization through Data Sharpening

拟议的研究旨在改进平滑数据的方法，以便更清楚地显示其中所含的信息。为了从数据中提取有用的信息，有必要对数据进行图形化的探索，特别是在有许多观测值的情况下。核平滑方法提供数据的图形摘要，允许数据分析师检测模式和变量之间可能的关系，并且以这样一种方式进行分析，几乎不需要做出假设，允许数据“为自己说话”。在许多情况下，关于数据的附加信息是可用的。例如，森林火灾燃烧的面积不会随着火灾燃烧的时间而减少。因此，在模拟野火的生长时，除了观测到的测量结果外，我们还可以使用这些信息。未经调整的标准技术通常会忽略这些信息，并且所得到的模型有时会产生与现实不符的异常情况。拟议研究的一个特别重点将放在数据锐化上，这是一种数据调整技术，利用有关数据的额外信息或产生数据的过程。然后将标准统计技术应用于调整后的数据，以便在不影响统计性能的情况下纳入给定的信息。计划是优化平滑的方法，并对使用数据锐化的统计推断方法进行全面调查。后一种技术将在诸如野火预测等应用中改进不确定性量化。数据锐化分为两类：“有监督”和“无监督”。在前者中，数据被移动了最小的距离，这取决于结果模型是否满足额外的信息。例如，我们可能希望最小限度地移动火灾大小测量值，以满足所得到的模型只预测火灾大小随时间增加的要求。无监督数据锐化并不直接结合外部信息，而是利用给定统计技术的属性来提出调整数据的规则，从而提高结果估计的准确性。对数据锐化及其变体进行彻底的调查是迟来的，因为该方法在一段时间前被提出，但根本没有得到充分的探索，并且因为它在改善各种统计方法的性能方面具有相当大的希望。提案中开发的方法也将立即用于重要应用，包括：研究空中加油机飞行员疲劳的潜在因素，其中研究了反应时间数据、生理变量和环境变量；金融信用风险问题；而且，正如上面提到的，由于野火等现象造成的环境风险。

The proposed research seeks to improve upon methods for smoothing data in order to more clearly visualize the information contained therein.  In order to extract useful information from data, it is necessary to explore it graphically, especially in situations where there are many observations.  Kernel smoothing methods provide graphical summaries of data which allow a data analyst to detect patterns and possible relationships between variables, and the analysis is done in such a way that very few assumptions need to be made, allowing the data to "speak for themselves''.    In many circumstances, additional information about the data is available.  For example, the area burned by a forest fire will not decrease over the time that the fire is burning.  Therefore, when modelling the growth of a wildfire, we could use this information in addition to observed measurements.  Standard techniques, without adjustment, usually ignore this information, and the resulting models can sometimes produce anomalies that do not match reality.  A particular focus of the proposed research will be on data sharpening which is a data-adjustment technique where extra information about the data, or the process that gave rise to the data, is exploited.  Standard statistical techniques are then applied to the adjusted data, so that the given information is incorporated, without compromising statistical performance. The plan is to optimize the methodology for smoothing and to launch a full-scale investigation into statistical inference methods that use data sharpening. The latter techniques will lead to improved uncertainty quantification in applications such as wildfire prediction.  Data sharpening falls into two categories: "supervised" and "unsupervised". In the former, data are moved a minimal distance, subject to the extra information being satisfied by the resulting model.  For example, we might want to move fire size measurements minimally, subject to the requirement that the resulting model only predicts that fire size increases over time.  Unsupervised data sharpening does not directly incorporate external information but rather works with properties of the given statistical technique to come up with rules for adjusting the data so that accuracy of the resulting estimate is improved.  A thorough investigation of data sharpening and its variants is overdue, since the methodology was proposed some time ago but not at all fully explored,  and since it holds considerable promise in terms of improving performance of a wide variety of statistical methods.  The methodologies developed in the proposal will also immediately be put to use in important applications including: a study of factors underlying airtanker pilot fatigue, where reaction time data, physiological variables, and environmental variables are studied; problems in financial credit risk; and, as alluded to above,  environmental risk due to phenomena such as wildfire.