Analysis and modeling spatiotemporal events on complex spatial regions

Chaudhuri, Somnath
Spatial statistics is traditionally based on stationary models like Matérn fields. However, applying stationary models to complex spatial regions having physical barriers like islands or coastal areas can result in inappropriate smoothing of such regions. Additionally, in many environmental applications such as stream systems or urban road networks, it is essential to define statistical models on linear networks. The current research thesis explores the benefits and limitations of integrated nested Laplace approximations (INLA) along with traditional stochastic partial differential equation (SPDE) for Bayesian spatiotemporal modeling. The study focuses on complex distributed spatial regions having physical barriers, as well as linear networks like urban road networks. The motivation behind the initial research article is to design an application to monitor the dynamics of COVID-19 pandemic in a spatiotemporal context in the region of Catalonia, Spain. In this case, we have used INLA-SPDE but in continuous spatial region. The following two articles involved utilizing explicit network triangulation to explore and analyse the occurrences of traffic accidents on urban road networks in UK and Spain. We proposed the novel concept of spatial triangulation restricted to linear networks. But complex boundary regions create fictitious spatial structures resulting in artificial spatial dependencies. In the following proposed articles, we have explored alternative computational strategies to design nonstationary barrier models. Initially, we have used barrier model to analyse spatial variation of tsunami risk in the Republic of Maldives. Then we implemented barrier models on linear networks. But in both cases, boundaries lie within the spatial domain of interest, preventing the high boundary effects from being reduced. The final proposed article presents a novel strategy for utilizing non-Euclidean metric on graph structures, as an alternative to the conventional Euclidean distance methodology. In this case, it is challenging to find flexible classes of functions that are positive definite to formulate Gaussian fields on metric graphs. Utilizing the mentioned concept, a novel category of Gaussian processes has been developed on compact metric graphs. The Whittle-Matérn fields employed in this approach are defined through a fractional SPDE on a metric graph. The proposed fields are a natural extension of Gaussian fields with Matérn covariance functions on Euclidean domains to non-Euclidean metric graph settings. A ten-year period (2010-2019) of daily traffic-accident records from Barcelona, Spain have been used to evaluate the three models referred above. While comparing model performance using evaluation metrics, we observed that the proposed fractional SPDE on metric graph model outperform network triangulation and barrier models. Due to this flexibility, it can be applied to a wide range of environmental issues, especially those involving complex or distributed spatial regions, such as islands, road networks, or areas demarcated by boundaries ​
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