Uncertainty quantification and design of experiments

不确定性量化和实验设计

• 批准号: 2481251
• 金额: --
• 依托单位: University of Manchester
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2481251
• 关键词: Uncertainty; quantification; design; experiments

Mechanistic and phenomenological models are used - often in the form of time-consuming computer simulations - across diverse areas of Science and Engineering to understand phenomena and make predictions and inferences, e.g. climate science, epidemiology, and radiological protection to name a few. Such models are informed by theory, but they usually also require data from experiments or observational studies on the real physical process in order to establish parameter values, identify the discrepancy between the model output and reality, and/or suggest potential model improvements. These experiments require careful design in order to yield maximum information about, or understanding of, the process. The major questions this research project will seek to answer are:-1) how best can we fit such models to the data given the uncertainty about the parameters and the discrepancy (or model error), and given that the models are often too computationally expensive for traditional methods to be used?2) how best can we design experiments and studies to provide the most informative data to support this model fitting?The scientific field of Uncertainty Quantification, on the border between Statistics and Applied Mathematics, has put forward several techniques for the first problem, one of the most popular being the method proposed by Kennedy and O'Hagan (2001) which uses Gaussian processes and Markov Chain Monte Carlo (MCMC) techniques to handle the various uncertainties in a Bayesian framework. Despite its popularity, this technique suffers from the problem of 'non-identifiability': essentially, it cannot tell which parts of the true phenomenon are due to the model and which are due to model error. We will develop advanced function-space MCMC techniques to enable a fully identifiable formulation to be established. We anticipate that this will both increase the accuracy and decrease the uncertainty of inferences made from the data and subsequent predictions from the model. Design of Experiments, a subfield of Statistics, gives many methods for optimizing the settings applied in an experiment in order to maximize the amount of information gained about a model. However, most existing results for physical experiments apply only to empirical models or computationally-inexpensive phenomenological models, not the expensive models underpinning modern simulations. In contrast, the design methods that apply to computationally-expensive models usually apply only to the simulations themselves (so called in silico experiments, or 'computer experiments'), not the physical experiments used to inform establish parameter values and estimate the model discrepancy. There are only a few published works on the design of the physical experiment for calibration of computationally expensive models, and none of these fully addresses the goals of both prediction and understanding in a coherent Bayesian framework, nor do these methods apply to the most up to date calibration methodology. Our work will seek to establish more comprehensive and up to date methodology by developing novel optimality criteria, utility approximations, and optimization techniques, and reflecting the latest developments in model-fitting approaches.The project will generate important original knowledge in Statistics, in the subfields of both Uncertainty Quantification and Design of Experiments, including new methods for inference and fitting of complex models and new methods for designing experiments to support this. Comparisons with existing methods will be developed to show the benefits of the new methodology. We expect the work developed will be publishable in top international Statistical journals such as Journal of the American Statistical Association and Technometrics. References Kennedy, M. C., & O'Hagan, A. (2001). Bayesian calibration of computer models. Journal of the Royal Statistical Society: Series B, 63, 425-464.

机械学和现象学模型通常以耗时的计算机模拟的形式在科学和工程的不同领域中使用，以了解现象并进行预测和推断，例如气候科学，流行病学和辐射防护等。这些模型是由理论提供信息的，但它们通常也需要来自对真实的物理过程的实验或观察研究的数据，以便建立参数值，识别模型输出与现实之间的差异，和/或建议潜在的模型改进。这些实验需要精心设计，以产生最大的信息，或理解，过程。本研究项目将寻求回答的主要问题是：1）考虑到参数和差异（或模型误差）的不确定性，以及考虑到模型通常计算成本太高，无法使用传统方法，我们如何才能最好地将这些模型与数据拟合？2)我们如何才能最好地设计实验和研究，以提供最翔实的数据，以支持这一模型拟合？不确定性量化的科学领域，在统计学和应用数学之间的边界，已经提出了几种技术来解决第一个问题，其中最流行的是Kennedy和O 'Hagan（2001）提出的方法，该方法使用高斯过程和马尔可夫链蒙特卡罗（MCMC）技术来处理贝叶斯框架中的各种不确定性。尽管这种技术很受欢迎，但它存在“不可识别性”的问题：本质上，它无法分辨真实现象的哪些部分是由于模型造成的，哪些是由于模型误差造成的。我们将开发先进的功能空间MCMC技术，以建立一个完全可识别的配方。我们预计，这将提高准确性，并降低从数据和模型的后续预测作出的推断的不确定性。实验设计是统计学的一个子领域，它提供了许多优化实验中应用的设置的方法，以最大限度地获得关于模型的信息量。然而，大多数现有的物理实验结果仅适用于经验模型或计算成本低廉的唯象模型，而不是支撑现代模拟的昂贵模型。相比之下，适用于计算昂贵的模型的设计方法通常仅适用于模拟本身（所谓的计算机实验或“计算机实验”），而不是用于通知建立参数值和估计模型差异的物理实验。只有少数已发表的作品的物理实验的设计计算昂贵的模型的校准，这些都没有完全解决的目标，预测和理解在一个连贯的贝叶斯框架，也不适用于这些方法最新的校准方法。我们的工作将寻求建立更全面和最新的方法，通过开发新的最优性准则，效用近似和优化技术，并反映模型拟合方法的最新发展。该项目将产生重要的原始知识统计，在不确定性量化和实验设计的子领域，包括推理和拟合复杂模型的新方法以及设计实验以支持这一点的新方法。将与现有方法进行比较，以显示新方法的好处。我们希望开发的工作将在顶级国际统计期刊上发表，如美国统计协会杂志和技术计量学。 参考文献Kennedy，M. C.的方法，& O'Hagan，A.（2001年）的第10页。计算机模型的贝叶斯校准。Journal of the皇家统计学会：系列B，63，425-464。