Deep Compositional Spatial Models

Spatial processes with nonstationary and anisotropic covariance structure are often used when modeling, analyzing, predicting complex environmental phenomena. Such may be expressed as ones that have stationary isotropic on a warped spatial domain. However, the warping function is generally difficult to fit not constrained injective, resulting in “space-folding.” Here, we propose modeling an injective through composition of multiple elemental functions deep-learning framework. We consider two cases; first, these known up some weights need estimated, and, second, each layer random. Inspired by recent methodological technological advances deep learning Gaussian processes, employ approximate Bayesian methods make inference models using graphics processing units. Through simulation studies one dimensions show compositional quick fit, able provide better predictions uncertainty quantification than other stochastic similar complexity. also their remarkable capacity model nonstationary, data radiances from MODIS instrument aboard Aqua satellite.