Estimation of Space Deformation Using Affine Coupling

Oregon Convention Center 

For modeling non-stationary spatial processes, spatial deformation is a popular approach in the literature, which characterizes the underlying non-stationary process as a stationary counterpart in the deformed space through proper space mapping. Existing studies often follow a two-step procedure, involving space mapping exploration in the initial step and spatial covariance estimation in the subsequent step. The first step typically involves estimating local variograms from data, followed by applying a multi-dimensional scaling technique with spline fittings to construct a smoothed deformed space. This study introduces a novel approach to estimate the space deformation, considering affine coupling for space mapping. The proposed method applies to both single and multiple realizations of spatial data where the spatial locations may vary across different realizations, offering flexibility and ensuring a bijective mapping. For inference, we use maximum likelihood to simultaneously estimate the deformation space mapping and the spatial covariance function. The effectiveness of the proposed method is demonstrated through simulations and real data examples.

Affine coupling

gradient descent

non-stationarity

regularization


spatial deformation 

Section on Statistics and the Environment