Baseline designs, space-filling designs and big data research

这项建议讨论了实验设计中的三个研究方向，实验设计是统计学中处理数据收集的一个分支。第一个方向是基线设计。析因设计在科学和技术中通常被用来研究响应变量如何依赖于一些潜在因素。通常使用正交效应进行分析，这称为正交参数化法。当因子具有默认设置时，效果的基线参数化变得更合适。基线效应的非正交性带来了严重的挑战，到目前为止，只有非常有限的结果可用。该提案将通过建立和利用两种类型的参数化之间的关系来审查一种新的方法。这一新方法有望取得丰硕的成果。下一个方向是空间填充设计。如今，科学技术调查经常在计算机上进行。对于复杂的计算机模型，构建代理模型以实现快速更新和预测是谨慎的。解决这个问题的统计学方法是通过计算机实验，研究人员根据一组输入和相应的输出建立代理模型。明智地选择投入至关重要。空间填充设计最适合计算机实验。最有吸引力的方法是使用强正交数组，因为它们有保证的空间填充特性。尽管最近取得了进展，但一些主要问题仍然悬而未决，这些问题是拟议研究的主题。一个例子是寻找在其他标准下也表现良好的强正交表，例如正交性、距离或差异。第三个方向是关于大数据研究。我们考虑了一个测量约束的监督学习问题。有一个包含对解释变量的观察的大数据集可用，但关于响应变量的信息获取起来非常昂贵。在这种情况下，必须选择大数据集的样本；然后可以收集关于这个小数据集的响应变量的信息。两种流行的方法是使用杠杆的抽样法和使用设计理论的确定性方法，称为IBOSS。虽然与抽样方法相比，IBOSS具有吸引人的特性，但它严重依赖于预先指定的线性模型。这项拟议的研究考察了空间填充设计对子数据选择的使用。该方法对模型错误描述具有较强的鲁棒性，并有望在不同的模型下表现良好。培训HQP是拟议研究的组成部分。上述三个研究方向中的每一个都有足够的主题来培养至少一名博士生。本研究还为培养本科生和硕士研究生提供了丰富的研究课题。HQP培训计划将详细说明如何将HQP培训纳入拟议的研究。

This proposal discusses three research directions in experimental design, a branch of statistics that deals with data collection. The first direction is on baseline designs. Factorial designs are commonly employed in science and technology to study how a response variable depends on a number of potential factors. Analysis is generally done using orthogonal effects, which is called the orthogonal parametrization. When factors have a default setting,  a baseline parametrization of effects becomes more appropriate. Nonorthogonality of baseline effects raises serious challenges, and only very limited results are available to this date. The proposal will examine a new approach by establishing and utilizing a relationship between the two types of parametrization. Rich results are expected from this novel approach. The next direction is on space-filling designs. Nowadays, scientific and technological investigations are routinely conducted on computers. For complex computer models, it is prudent to build a surrogate model for fast updating and predictions. The statistical approach to this problem is via computer experiments, where researchers build surrogate models based on a set of inputs and corresponding outputs. Judicious selection of inputs is crucial. Space-filling designs are most suited for computer experiments. The most attractive approach is to use strong orthogonal arrays because of their guaranteed space-filling properties. Despite recent advances, some major problems remain open and they are topics for the proposed research. One example is to find strong orthogonal arrays that also perform well under other criteria such as those of orthogonality, distance or discrepancy.  The third direction is about big data research. We consider a measurement constrained supervised learning problem. A big data set is available that contains observations on explanatory variables, but information on a response variable is very expensive to obtain. This situation necessitates the selection of a sample of the big data set; one can then collect information on the response variable for this small data set. Two popular methods are a sampling method using leverages and a deterministic method, called IBOSS, using design theory. While the IBOSS enjoys appealing properties compared to the sampling method, it heavily relies on a pre-specified linear model. The proposed research examines the use of space-filling designs for subdata selection. This approach is robust to model misspecification, and expected to perform well under various models. Training HQP is integral part of the proposed research. Each of the three research directions outlined above has enough topics to train at least one PhD student. The proposed research also contains a plentiful supply of research topics for training undergraduate and MSc students. Details on how to integrate HQP training into the proposed research will be provided in the HQP training plan.