Fast Estimation of non-Gaussian Fields

Oregon Convention Center 

Data derived from remote sensing or from the output of numerical simulations typically has some regular gridded structure but is large in volume. The challenge is to find accurate spatial models to fill in missing grid cells or emulate the process in the presence of heterogeneity of the spatial fields and heavy tailed marginal distributions. A spatial autoregressive model is a map from a location and its neighbors to spatially independent random variables and can provide a flexible model for non-Gaussian fields. This can be accomplished using distributions of innovations with heavy tails and maps that are nonlinear in combining the central location with its neighbors. These models are fast to simulate by taking advantage of the sparseness of the map, but the estimation is slow for large data fields. An alternative to traditional statistical methods is to train a neural network based on a large training set spanning a useful parameter space and then use the network for fast estimation. This approach is applied to high resolution ecologic data from the JPL SHIFT mission and also from numerical simulations of urban flooding under different storm forcings.