Baseline designs, space-filling designs and big data research

实验设计是统计学中处理数据收集的一个分支，本文讨论了实验设计的三个研究方向。第一个方向是基线设计。析因设计通常用于科学和技术，以研究反应变量如何依赖于许多潜在因素。分析一般采用正交效应，称为正交参数化。当因子具有默认设置时，效果的基线参数化变得更加合适。基线效应的非正交性提出了严峻的挑战，迄今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参数化之间的关系来审查一种新的方法。这种新颖的方法有望带来丰富的结果。下一个方向是空间填充设计。如今，科学和技术调查通常是在计算机上进行的。对于复杂的计算机模型，为快速更新和预测构建代理模型是明智的。解决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替代模型。明智地选择投入至关重要。空间填充设计最适合于计算机实验。最吸引人的方法是使用强正交阵列，因为它们保证了空间填充特性。尽管最近取得了进展，但一些主要问题仍未解决，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，如正交性、距离或差异。第三个方向是关于大数据的研究。我们考虑一个测量约束的监督学习问题。一个大的数据集是可用的，其中包含了对解释变量的观察，但是关于响应变量的信息是非常昂贵的。这种情况需要从大数据集中选取样本；然后就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。提出的研究考察了子数据选择中空间填充设计的使用。该方法对模型错误规范具有鲁棒性，并期望在各种模型下都能表现良好。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。建议的研究也包含了丰富的研究课题，以培养本科生和硕士生。关于如何将HQP培训纳入拟议研究的细节将在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.