Computer Experiments and Multi-stage Factorial Designs

计算机实验和多阶段因子设计

• 批准号: 355995-2013
• 负责人: Ranjan, Pritam
• 金额: $ 1.09万
• 依托单位: Acadia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=572710
• 关键词: Computer; Experiments; Multi; stage; Factorial

My research program will focus on the design and analysis of (a) computer experiments and (b) multi-stage factorial experiments with randomization restrictions. Computer simulators are often used to model extremely expensive or unobservable complex physical systems. Realistic simulators of complex processes can still be expensive to run, and a statistical surrogate is used for experimentation. Important current research topics include surrogate modeling, design of experiments, integrating various sources of data, inverse problem and uncertainty quantification (an emerging area). Dynamic computer simulators is an active research area, and scientists are interested in efficient designs for estimating process features (e.g., global minimum, contour). I am proposing innovative ideas for generalizing my contour estimation method (for scalar valued simulators) to solve the inverse problem when the simulator returns a time series output. As part of this research program, I will invent new surrogates for simulators that cannot be emulated by conventional Gaussian process models. For instance, I am developing a new hierarchical Gamma process model with Gaussian latent variables for emulating simulators with positive responses. The existence and construction of designs for multi-stage factorial experiments with randomization restrictions (e.g., split-lot designs) is a challenging problem. I proposed a finite projective geometry (PG) approach which establishes the existence results and facilitates easy construction of such designs via spread (partition into subspaces) and stars (subspaces with common overlap) of PG. My proposed research will focus of finding optimal fractional factorial designs under this unified framework. More interestingly, I have discovered a new class of Latin hypercube designs (LHDs) that can be constructed from stars. These designs have geometric properties that are useful for generating space-filling LHDs, a very popular design in computer experiments.

我的研究计划将集中在（a）计算机实验和（B）随机化限制的多阶段析因实验的设计和分析。 计算机模拟器通常用于模拟极其昂贵或不可观测的复杂物理系统。复杂过程的现实模拟器运行起来仍然很昂贵，并且使用统计替代品进行实验。当前重要的研究课题包括替代建模、实验设计、整合各种数据源、逆问题和不确定性量化（一个新兴领域）。 动态计算机模拟器是一个活跃的研究领域，科学家们对用于估计过程特征的有效设计感兴趣（例如，全局最小值，轮廓）。我提出了创新的想法，推广我的轮廓估计方法（标量值模拟器），以解决模拟器返回时间序列输出时的逆问题。作为这项研究计划的一部分，我将发明新的模拟器，不能用传统的高斯过程模型来模拟。例如，我正在开发一个新的分层伽马过程模型，具有高斯潜变量，用于模拟具有积极响应的模拟器。 具有随机化限制的多阶段析因试验设计的存在性和构造（例如，分批设计）是一个具有挑战性的问题。我提出了一个有限射影几何（PG）的方法，建立存在性的结果，并通过传播（划分成子空间）和星（子空间与公共重叠）的PG，我建议的研究将集中在寻找最佳的分数析因设计的存在性，并方便容易建设。更有趣的是，我发现了一类新的拉丁超立方体设计（LHD），可以从恒星构造。这些设计的几何属性，是有用的生成空间填充LHD，在计算机实验中非常流行的设计。