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Abstract:
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Analyzing large spatio-temporal data sets proves to be computationally challenging due to the need to invert large dense matrices. To get around this, researchers will typically use either sparsity or reduced rank approaches to reduce the dimensionality. In a dynamic spatio-temporal model with discrete time, the sparsity is significantly diluted as the model updates from one time point to the next. This work presents a particular parameterization of an advection-diffusion stochastic partial differential equation called implied advection that allows for a dynamic spatio-temporal model to be constructed and fit without the sparsity being diluted over time. Using dynamic modeling tricks such as discount factors and a nearest neighbor Gaussian process for the sparsity, the entire model can be fit without ever inverting a dense matrix. This model is illustrated on Pacific sea surface temperature data where using a non-linear stochastic partial differential equation leads to a non-linear dynamic spatio-temporal model.
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