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

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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.