Deep Compositional Spatial Models for Nonstationary Extremal Dependence

Music City Center 

Modeling the nonstationarity that often prevails in extremal dependence of spatial data can be challenging. Inference for stationary and isotropic models is considerably easier, but the assumptions that underpin these models are not typically met by data observed over large or topographically complex domains. A simple approach to accommodating spatial nonstationarity under the assumption of Gaussianity is to warp the original spatial domain to a latent space where stationarity and isotropy can be reasonably assumed and has since seen further developments in the classical Gaussian-based geostatistics and spatial extremes contexts. However, estimation of the warping function can be computationally expensive, and the transformation is not always guaranteed to be injective, which can lead to physically unrealistic transformations. We present a deep compositional model to capture nonstationarity in extremal dependence in exceedances of data functionals by leveraging efficient inference methods for r-Pareto processes. A detailed high-dimensional simulation study demonstrates the superior performance of our model in estimating the warped space, leading to an accurate characterization of the highly nonstationary extremal dependence structure. We apply the proposed approach to UK precipitation data, where we efficiently estimate the extremal dependence pattern with data observed at thousands of locations, which has never been achieved in previous relevant studies. The model is programmed with the R language and tensorflow v2.

Deformation

Nonstationarity

Deep Models

Spatial Extremes

r-Pareto Processes