Robust, Scalable Sequential Monte Carlo with Application To Urban Air Quality

这个项目是由两个实质性的考虑驱动的：在大型复杂系统中，迫切需要进行推断的方法，即估计间接观测系统的参数。现有技术通常不能很好地扩展到在许多现代数据丰富的背景下出现的非常大的数据集。大多数最近的发展，旨在提高现有算法的可扩展性的计算统计学集中在数据，具有非常特殊的形式，特别是可以被看作是非常大的数量的重复测量是相互独立的。这种方法不适合具有强的空间和时间结构的数据集，例如，在城市分析环境中获得的许多数据集。该项目旨在开发一套方法工具，通过利用模型的结构，以同时提供有效的计算工具和良好的估计，以计算有效的方式在这类模型中进行推理。此外，利用稳健统计领域的最新发展，这些方法将适用于处理建模不完善和数据生成过程不完全具有数学模型特征的情况。这种鲁棒性对于在真实的复杂场景中获得良好的性能至关重要。空气质量监测是一个非常重要和非常具有挑战性的领域。不同的传感器网络存在于不同的尺度上，并提供彼此具有完全不同特性的测量。随着观测结果变得可用，融合这些信息是一个大规模的统计推断问题。事实上，这种类型的问题激发了这个项目的方法发展，并将作为一个广泛的试验台开发的方法。在大伦敦管理局的支持下，将这些方法扩大应用于大伦敦地区的空气质量监测，这是本建议的第二个主要方面。

This project is driven by two substantial considerations.Methods for conducting inference, i.e. estimating the parameters of an indirectly observed system, in large complex systems are urgently needed. Existing technology does not generally scale well to the very large data sets which arise in many modern data-rich contexts. Most of the recent developments in computational statistics which aim at improving the scalability of existing algorithms have focused on data which has very particular forms and in particular can be viewed as very large numbers of replicates of measurements which are independent of one another. Such methods are not suitable for data sets which have strong spatial and temporal structures as, for example, many data sets obtained in urban analytic settings do. This project aims to develop a suite of methodological tools for conducting inference in models of this sort in a computationally efficient way, by exploiting the structure of the models in order to provide simultaneously efficient computational tools and good estimation. Furthermore, leveraging recent developments in the field of robust statistics, these methods will be adapted to deal with settings in which the modelling is imperfect and the data generating process is not exactly characterized by the mathematical model. This robustness is essential to obtain good performance in real, complex scenarios.Air quality monitoring is a tremendously important and tremendously challenging area. Diverse sensor networks exist on different scales and provide measurements with quite different characteristics to one another. Fusing this information as observations become available is a large scale statistical inference problem. Indeed, problems of this type motivate the methodological development of this project and will serve as an extensive test-bed for the developed methodology. An extended application of those methods to air quality monitoring in the Greater London area with the support of the Greater London Authority provides the second major aspect of this proposal.