Modeling Spatial Extremes using Non-Gaussian Spatial Autoregressive Models via Convolutional Neural Networks

Music City Center 

Data derived from remote sensing or numerical simulations often have a regular gridded structure and are large in volume. However, it is challenging to find accurate spatial models that can fill in missing grid cells or simulate the process effectively, especially when there is spatial heterogeneity and heavy-tailed marginal distributions. One effective method is to use a spatial autoregressive (SAR) model, which maps a location and its neighbors to spatially independent random variables. This model is flexible and well-suited for non-Gaussian fields. In this study, we assume that the innovations in the SAR model follow a Generalized Extreme Value (GEV) distribution, a heavy-tailed distribution, and incorporate nonlinear maps that combine a central grid location with its neighbors, introducing extreme spatial behavior. While these models are fast to simulate due to the sparseness of the construction, the estimation process is slow because the likelihood is intractable. To overcome this, we suggest training a convolutional neural network (CNN) on a large training set that covers a useful parameter space and then using the trained network for fast estimation. We apply this model to analyze yearly maximum precipitation data from a regional climate model to study spatial extremal behavior across North America.

Spatial Autoregressive Model

Generalized Extreme Value Distribution

Convolutional Neural Networks

Parameter Estimation

Spatial Extremes

Quantile Regression