Modeling Spatial Extremes using Non-Gaussian Spatial Autoregressive Models via Convolutional Neural Networks
This provides a computationally efficient method for researchers analyzing spatial extremes in environmental data like precipitation, though it is incremental as it combines existing SAR and CNN approaches.
The authors tackled the challenge of modeling spatial extremes in large gridded datasets by developing a spatial autoregressive framework with Generalized Extreme Value innovations, and overcame computational intractability by training a convolutional neural network for fast parameter estimation. They applied this model to annual maximum precipitation data across North America, demonstrating its capability to capture extreme spatial behavior.
Data derived from remote sensing or numerical simulations often have a regular gridded structure and are large in volume, making it challenging to find accurate spatial models that can fill in missing grid cells or simulate the process effectively, especially in the presence of spatial heterogeneity and heavy-tailed marginal distributions. To overcome this issue, we present a spatial autoregressive modeling framework, which maps observations at a location and its neighbors to independent random variables. This is a highly flexible modeling approach and well-suited for non-Gaussian fields, providing simpler interpretability. In particular, we consider the SAR model with Generalized Extreme Value distribution innovations to combine the observation at a central grid location with its neighbors, capturing extreme spatial behavior based on the heavy-tailed innovations. While these models are fast to simulate by exploiting the sparsity of the key matrices in the computations, the maximum likelihood estimation of the parameters is prohibitive due to the intractability of the likelihood, making optimization challenging. To overcome this, we train a convolutional neural network on a large training set that covers a useful parameter space, and then use the trained network for fast parameter estimation. Finally, we apply this model to analyze annual maximum precipitation data from ERA-Interim-driven Weather Research and Forecasting (WRF) simulations, allowing us to explore its spatial extreme behavior across North America.