Adaptive design of experiments for spatio-temporal models

时空模型实验的自适应设计

• 批准号: EP/E009905/1
• 负责人: Alexander Dolia
• 金额: $ 30.91万
• 依托单位: University of Southampton
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2007
• 资助国家: 英国
• 起止时间: 2007 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FE009905%2F1
• 关键词: Adaptive; design; experiments; spatio; temporal

Recall the last weather forecast map you saw on television. The map shows how aspects of the weather vary both in space and time. It is important to be able to predict and understand, such response variables that describe the weather, for example the amount of rainfall, sunshine and air pollution. There are many other important areas that affect our day-to-day lives in which spatio-temporal data are used to detect recognisable and meaningful patterns as well as to make predictions. Examples include the study of house prices, ecology, geology and many areas of medicine such as brain imaging.In order to obtain high accuracy in predictions of a response variable and to gain scientific insights into how the response is varying with space and time, mathematical models that are statistical in nature are employed which explicitly include the underlying uncertainty in the data. This research is concerned with such models and how to plan experiments to gather data in the most effective and efficient way. Designs are considered which are adaptive in the sense that data gathered at previous time points and locations are used to inform the choice of locations where observations are to be made at the next time point. A number of requirements on such a design are investigated, such as high accuracy of predictions and sound interpretation of the model that will be fitted to the data. These requirements are translated into criteria, including multi-objective criteria, for selecting the locations for the next time point using a Bayesian framework. Algorithms for finding the design are developed and implemented.

回想一下你在电视上看到的最后一张天气预报图。这张地图显示了天气在空间和时间上的变化。重要的是能够预测和理解描述天气的响应变量，例如降雨量，阳光和空气污染。还有许多其他影响我们日常生活的重要领域，其中时空数据用于检测可识别和有意义的模式以及进行预测。例如房价、生态学、地质学和许多医学领域的研究，如脑成像。为了获得响应变量预测的高准确性，并获得响应如何随空间和时间变化的科学见解，采用本质上是统计的数学模型，其中明确包括数据中的潜在不确定性。本研究关注的是这样的模型，以及如何计划实验，以最有效和最高效的方式收集数据。设计被认为是自适应的，在这个意义上，在以前的时间点和位置收集的数据被用来通知在下一个时间点进行观察的位置的选择。对这种设计的一些要求进行了研究，如预测的高精度和将拟合数据的模型的合理解释。这些要求被转化为标准，包括多目标标准，用于使用贝叶斯框架选择下一个时间点的位置。算法找到设计的开发和实施。