Statistical Learning of High-Dimensional Spatial Dependence Structures

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The project deals with an important, fundamental problem of spatial and spatiotemporal statistics – the full estimation of the underlying spatial dependence structure. For these models, the focus has so far been on processes showing a dependence in the conditional means. That is, the mean of a realization of the random process at a particular measurement point depends on the adjacent observations. This finding goes back to the Tobler’s first law of Geography. The surrounding observations are defined on the basis of their geographical proximity, although this does not necessarily lead to a dependence of the observations of the random variables, i.e. the covariances.Both geostatistical and spatial econometric models assume a certain structure of the spatial dependence, which, however, is typically unknown. In this project, therefore, new statistical methods will be developed that allow the complete estimation of the spatial dependence structure. For this purpose, machine/statistical learning methods will be used.Besides classical models with (autoregressive) dependencies in the conditional means, models with dependencies in conditional variances will be investigated. These models are so-called spatial ARCH processes - analogous to the temporal ARCH model of Robert F. Engle (1982).Finally, various application examples will be used to demonstrate how the estimated parameters can be interpreted. Here, the focus will be on natural processes in the environment, such as air pollution or particulate matter. Using freely available sensor data, the results can be used, for example, to obtain local predictions of fine dust pollution in an urban area, which can then be used for optimal routing with respect to air quality.