Baseline designs, space-filling designs and big data research

这个建议讨论了实验设计的三个研究方向，实验设计是统计学的一个分支，主要处理数据收集。 第一个方向是基线设计。析因设计通常用于科学和技术研究响应变量如何取决于许多潜在因素。通常使用正交效应进行分析，这称为正交参数化。当因子具有默认设置时，效应的基线参数化变得更合适。基线效应的非正交性提出了严重的挑战，迄今为止只有非常有限的结果。该提案将审查一种新的办法，建立和利用两种参数化之间的关系。这种新颖的方法有望获得丰富的结果。 下一个方向是空间填充设计。如今，科学和技术调查通常在计算机上进行。对于复杂的计算机模型，谨慎的做法是构建代理模型以进行快速更新和预测。这个问题的统计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。明智地选择输入至关重要。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表，因为它们保证了空间填充特性。尽管最近取得了进展，但一些主要问题仍然存在，它们是拟议研究的主题。一个例子是找到在其他标准下也表现良好的强正交阵列，例如正交性，距离或差异。 第三个方向是大数据研究。我们考虑一个测量约束的监督学习问题。一个大数据集是可用的，其中包含对解释变量的观察，但对响应变量的信息是非常昂贵的获得。这种情况需要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方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。拟议的研究探讨使用空间填充设计的子数据选择。该方法对模型误指定具有鲁棒性，并有望在各种模型下表现良好。 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。拟议的研究还包含了大量的研究课题，为培养本科生和硕士生。关于如何将HQP培训整合到拟议研究中的详细信息将在HQP培训计划中提供。

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.