The Statistical Design and Analysis of Experiments for Large-scale Computer Simulators

最近计算能力的提高提高了我们模拟复杂物理现象的能力。有了这些成果，就有可能研究历史上只有通过昂贵的物理实验才能解决的科学问题，如果有的话。通过计算模型探索复杂系统的例子在科学中很常见，最近的应用范围从天体物理学到气候变化再到微观生物的研究，等等，这样的例子不胜枚举。事实上，最近政府间气候变化专门委员会（IPCC）的报告包含了几个结论，这些结论是基于使用计算模型对现实世界的推断。在某些应用中，系统仿真的计算成本很高，因此选择模型的输入（实验设计）是研究的关键任务。在其他情况下，兴趣在于将模拟和现场数据结合起来。尽管如此，在其他情况下，模拟器可能很快，但模型运行的数量可能很高。无论如何，有许多科学家和工业研究人员感兴趣的紧迫问题需要解决，以便有效地利用他们的计算机模型。拟议的研究将为计算机实验开发新的统计方法。具体项目包括：(i)确定性计算机模拟器的建模输出；（ii）结合现场数据和离散数据的计算机模型输出，对物理过程进行推断；以及（iii）模拟大型模拟器运行集合。将提出具有良好空间填充性能的新实验设计。这些设计基于一般的晶格结构，这也将使研究计算机实验的标准建模方法成为可能。这项工作的预期结果将是在科学和工业中使用的实用方法，以及导致计算机实验进行方式变化的理论工作。在这个项目中进行的研究主要是由与科学家和工程师合作产生的问题所驱动的。拟议工作的所有方面都包括受训人员。

Recent gains in computational power have increased our ability to simulate complex physical phenomena. With these gains comes the potential to investigate scientific questions that historically would have been addressed only through expensive physical experimentation, if at all. Examples of exploration of complex systems via computational models is common in science, with recent applications ranging from astrophysics to climate change to the study micro-scale organisms, etc., the list goes on and on. In fact, the recent Intergovernmental Panel on Climate Change (IPCC) report contains several conclusions that are based on inference to the real world using computational models.In some applications, simulation of the system is computationally expensive making the choice of inputs (the experimental design) to the model a critical task of the study. In other settings, interest lies in combining simulations and field data. Still, in other situations, the simulator may be fast, but the number of model runs can be high. In any case, there are many pressing problems of interest to scientists and industrial researchers that need to be addressed to effectively utilize their computer models.The proposed research will develop new statistical methodology for computer experiments. Specific projects include (i) modeling output from deterministic computer simulators; (ii) combining field data and computer model outputs for discrete data to make inferences about physical processes; and (iii) modeling large ensembles of simulator runs. New experimental designs will be proposed that have good space-filling properties. The designs are based on a general lattice structure that will also enable investigation of standard modeling approaches for computer experiments. The anticipated outcomes of this work will be practical methodology to be used in science and industry, as well as theoretical work that leads to changes in the manner in which computer experiments are conducted. The research addressed in this program is heavily motivated by problems arising from collaboration with scientists and engineers. All aspects of the proposed work include trainees.